LMFDB - Embedded newform 1089.2.e.p.364.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			364.4
Character	$\chi$	$=$	1089.364
Dual form			1089.2.e.p.727.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.773068 - 1.33899i) q^{2} +(1.56806 + 0.735660i) q^{3} +(-0.195269 + 0.338216i) q^{4} +(-0.296016 + 0.512715i) q^{5} +(-0.227172 - 2.66833i) q^{6} +(-0.360975 - 0.625227i) q^{7} -2.48845 q^{8} +(1.91761 + 2.30711i) q^{9} +0.915362 q^{10} +(-0.555005 + 0.386690i) q^{12} +(0.787482 - 1.36396i) q^{13} +(-0.558117 + 0.966687i) q^{14} +(-0.841354 + 0.586199i) q^{15} +(2.31428 + 4.00845i) q^{16} +4.59200 q^{17} +(1.60677 - 4.35122i) q^{18} +2.50860 q^{19} +(-0.115606 - 0.200235i) q^{20} +(-0.106075 - 1.24595i) q^{21} +(2.22600 - 3.85554i) q^{23} +(-3.90203 - 1.83065i) q^{24} +(2.32475 + 4.02658i) q^{25} -2.43511 q^{26} +(1.30967 + 5.02840i) q^{27} +0.281949 q^{28} +(-3.48931 - 6.04366i) q^{29} +(1.43534 + 0.673395i) q^{30} +(4.56412 - 7.90529i) q^{31} +(1.08974 - 1.88749i) q^{32} +(-3.54993 - 6.14866i) q^{34} +0.427418 q^{35} +(-1.15475 + 0.198058i) q^{36} +2.89170 q^{37} +(-1.93932 - 3.35900i) q^{38} +(2.23823 - 1.55945i) q^{39} +(0.736620 - 1.27586i) q^{40} +(0.577060 - 0.999497i) q^{41} +(-1.58631 + 1.10524i) q^{42} +(2.10724 + 3.64985i) q^{43} +(-1.75053 + 0.300244i) q^{45} -6.88340 q^{46} +(0.113778 + 0.197069i) q^{47} +(0.680067 + 7.98800i) q^{48} +(3.23939 - 5.61079i) q^{49} +(3.59438 - 6.22565i) q^{50} +(7.20052 + 3.37815i) q^{51} +(0.307542 + 0.532678i) q^{52} -5.70359 q^{53} +(5.72053 - 5.64093i) q^{54} +(0.898268 + 1.55585i) q^{56} +(3.93363 + 1.84548i) q^{57} +(-5.39495 + 9.34433i) q^{58} +(-3.56678 + 6.17784i) q^{59} +(-0.0339715 - 0.399026i) q^{60} +(-2.27948 - 3.94817i) q^{61} -14.1135 q^{62} +(0.750262 - 2.03175i) q^{63} +5.88733 q^{64} +(0.466215 + 0.807507i) q^{65} +(4.04571 - 7.00738i) q^{67} +(-0.896676 + 1.55309i) q^{68} +(6.32686 - 4.40814i) q^{69} +(-0.330423 - 0.572310i) q^{70} -12.3094 q^{71} +(-4.77187 - 5.74113i) q^{72} +15.4833 q^{73} +(-2.23548 - 3.87196i) q^{74} +(0.683144 + 8.02414i) q^{75} +(-0.489852 + 0.848448i) q^{76} +(-3.81839 - 1.79141i) q^{78} +(7.30978 + 12.6609i) q^{79} -2.74025 q^{80} +(-1.64555 + 8.84829i) q^{81} -1.78443 q^{82} +(3.47650 + 6.02148i) q^{83} +(0.442113 + 0.207419i) q^{84} +(-1.35931 + 2.35439i) q^{85} +(3.25808 - 5.64316i) q^{86} +(-1.02536 - 12.0438i) q^{87} +12.4803 q^{89} +(1.75531 + 2.11185i) q^{90} -1.13705 q^{91} +(0.869338 + 1.50574i) q^{92} +(12.9724 - 9.03831i) q^{93} +(0.175916 - 0.304695i) q^{94} +(-0.742586 + 1.28620i) q^{95} +(3.09733 - 2.15801i) q^{96} +(-7.09023 - 12.2806i) q^{97} -10.0171 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) $ 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.773068	−	1.33899i	−0.546642	−	0.946811i	−0.998502	−	0.0547224i	$-0.982573\pi$
$2$	−0.773068	−	1.33899i	−0.546642	−	0.946811i	0.451860	−	0.892089i	$-0.350761\pi$
$3$	1.56806	+	0.735660i	0.905318	+	0.424733i
$3$	1.56806	+	0.735660i	0.905318	+	0.424733i
$4$	−0.195269	+	0.338216i	−0.0976345	+	0.169108i
$5$	−0.296016	+	0.512715i	−0.132382	+	0.229293i	−0.924594	−	0.380953i	$-0.875596\pi$
$5$	−0.296016	+	0.512715i	−0.132382	+	0.229293i	0.792212	+	0.610246i	$0.208929\pi$
$6$	−0.227172	−	2.66833i	−0.0927424	−	1.08934i
$7$	−0.360975	−	0.625227i	−0.136436	−	0.236314i	0.789709	−	0.613481i	$-0.210231\pi$
$7$	−0.360975	−	0.625227i	−0.136436	−	0.236314i	−0.926145	+	0.377168i	$0.876898\pi$
$8$	−2.48845			−0.879799
$9$	1.91761	+	2.30711i	0.639203	+	0.769038i
$10$	0.915362			0.289463
$11$		0			0
$11$		0			0
$12$	−0.555005	+	0.386690i	−0.160216	+	0.111628i
$13$	0.787482	−	1.36396i	0.218408	−	0.378294i	−0.735913	−	0.677076i	$-0.763247\pi$
$13$	0.787482	−	1.36396i	0.218408	−	0.378294i	0.954322	+	0.298782i	$0.0965802\pi$
$14$	−0.558117	+	0.966687i	−0.149163	+	0.258358i
$15$	−0.841354	+	0.586199i	−0.217237	+	0.151356i
$16$	2.31428	+	4.00845i	0.578570	+	1.00211i
$17$	4.59200			1.11372			0.556862	−	0.830605i	$-0.312005\pi$
$17$	4.59200			1.11372			0.556862	+	0.830605i	$0.312005\pi$
$18$	1.60677	−	4.35122i	0.378719	−	1.02559i
$19$	2.50860			0.575512			0.287756	−	0.957704i	$-0.407091\pi$
$19$	2.50860			0.575512			0.287756	+	0.957704i	$0.407091\pi$
$20$	−0.115606	−	0.200235i	−0.0258502	−	0.0447738i
$21$	−0.106075	−	1.24595i	−0.0231475	−	0.271888i
$22$		0			0
$23$	2.22600	−	3.85554i	0.464153	−	0.803937i	−0.535010	−	0.844846i	$-0.679692\pi$
$23$	2.22600	−	3.85554i	0.464153	−	0.803937i	0.999163	+	0.0409092i	$0.0130255\pi$
$24$	−3.90203	−	1.83065i	−0.796498	−	0.373680i
$25$	2.32475	+	4.02658i	0.464950	+	0.805317i
$26$	−2.43511			−0.477564
$27$	1.30967	+	5.02840i	0.252046	+	0.967715i
$28$	0.281949			0.0532834
$29$	−3.48931	−	6.04366i	−0.647949	−	1.12228i	−0.983612	−	0.180298i	$-0.942294\pi$
$29$	−3.48931	−	6.04366i	−0.647949	−	1.12228i	0.335663	−	0.941982i	$-0.391040\pi$
$30$	1.43534	+	0.673395i	0.262056	+	0.122945i
$31$	4.56412	−	7.90529i	0.819740	−	1.41983i	−0.0861334	−	0.996284i	$-0.527451\pi$
$31$	4.56412	−	7.90529i	0.819740	−	1.41983i	0.905874	−	0.423548i	$-0.139216\pi$
$32$	1.08974	−	1.88749i	0.192641	−	0.333664i
$33$		0			0
$34$	−3.54993	−	6.14866i	−0.608808	−	1.05449i
$35$	0.427418			0.0722468
$36$	−1.15475	+	0.198058i	−0.192459	+	0.0330096i
$37$	2.89170			0.475392			0.237696	−	0.971340i	$-0.423608\pi$
$37$	2.89170			0.475392			0.237696	+	0.971340i	$0.423608\pi$
$38$	−1.93932	−	3.35900i	−0.314599	−	0.544902i
$39$	2.23823	−	1.55945i	0.358403	−	0.249711i
$40$	0.736620	−	1.27586i	0.116470	−	0.201732i
$41$	0.577060	−	0.999497i	0.0901216	−	0.156095i	−0.817441	−	0.576013i	$-0.804608\pi$
$41$	0.577060	−	0.999497i	0.0901216	−	0.156095i	0.907562	+	0.419918i	$0.137941\pi$
$42$	−1.58631	+	1.10524i	−0.244773	+	0.170542i
$43$	2.10724	+	3.64985i	0.321351	+	0.556596i	0.980767	−	0.195182i	$-0.0625297\pi$
$43$	2.10724	+	3.64985i	0.321351	+	0.556596i	−0.659416	+	0.751778i	$0.729196\pi$
$44$		0			0
$45$	−1.75053	+	0.300244i	−0.260954	+	0.0447577i
$46$	−6.88340			−1.01490
$47$	0.113778	+	0.197069i	0.0165962	+	0.0287454i	0.874204	−	0.485558i	$-0.161384\pi$
$47$	0.113778	+	0.197069i	0.0165962	+	0.0287454i	−0.857608	+	0.514304i	$0.828050\pi$
$48$	0.680067	+	7.98800i	0.0981592	+	1.15297i
$49$	3.23939	−	5.61079i	0.462771	−	0.801542i
$50$	3.59438	−	6.22565i	0.508322	−	0.880440i
$51$	7.20052	+	3.37815i	1.00828	+	0.473036i
$52$	0.307542	+	0.532678i	0.0426484	+	0.0738691i
$53$	−5.70359			−0.783449			−0.391724	−	0.920083i	$-0.628121\pi$
$53$	−5.70359			−0.783449			−0.391724	+	0.920083i	$0.628121\pi$
$54$	5.72053	−	5.64093i	0.778465	−	0.767634i
$55$		0			0
$56$	0.898268	+	1.55585i	0.120036	+	0.207909i
$57$	3.93363	+	1.84548i	0.521022	+	0.244439i
$58$	−5.39495	+	9.34433i	−0.708392	+	1.22697i
$59$	−3.56678	+	6.17784i	−0.464355	+	0.804286i	−0.999172	−	0.0406816i	$-0.987047\pi$
$59$	−3.56678	+	6.17784i	−0.464355	+	0.804286i	0.534817	+	0.844968i	$0.320380\pi$
$60$	−0.0339715	−	0.399026i	−0.00438570	−	0.0515140i
$61$	−2.27948	−	3.94817i	−0.291857	−	0.505512i	0.682392	−	0.730987i	$-0.260940\pi$
$61$	−2.27948	−	3.94817i	−0.291857	−	0.505512i	−0.974249	+	0.225475i	$0.927607\pi$
$62$	−14.1135			−1.79242
$63$	0.750262	−	2.03175i	0.0945241	−	0.255977i
$64$	5.88733			0.735917
$65$	0.466215	+	0.807507i	0.0578268	+	0.100159i
$66$		0			0
$67$	4.04571	−	7.00738i	0.494262	−	0.856087i	−0.505716	−	0.862700i	$-0.668772\pi$
$67$	4.04571	−	7.00738i	0.494262	−	0.856087i	0.999978	+	0.00661279i	$0.00210493\pi$
$68$	−0.896676	+	1.55309i	−0.108738	+	0.188340i
$69$	6.32686	−	4.40814i	0.761665	−	0.530677i
$70$	−0.330423	−	0.572310i	−0.0394931	−	0.0684041i
$71$	−12.3094			−1.46086			−0.730429	−	0.682989i	$-0.760680\pi$
$71$	−12.3094			−1.46086			−0.730429	+	0.682989i	$0.760680\pi$
$72$	−4.77187	−	5.74113i	−0.562370	−	0.676599i
$73$	15.4833			1.81219			0.906093	−	0.423078i	$-0.139050\pi$
$73$	15.4833			1.81219			0.906093	+	0.423078i	$0.139050\pi$
$74$	−2.23548	−	3.87196i	−0.259869	−	0.450107i
$75$	0.683144	+	8.02414i	0.0788827	+	0.926548i
$76$	−0.489852	+	0.848448i	−0.0561899	+	0.0973237i
$77$		0			0
$78$	−3.81839	−	1.79141i	−0.432348	−	0.202838i
$79$	7.30978	+	12.6609i	0.822414	+	1.42446i	0.903880	+	0.427787i	$0.140707\pi$
$79$	7.30978	+	12.6609i	0.822414	+	1.42446i	−0.0814654	+	0.996676i	$0.525960\pi$
$80$	−2.74025			−0.306370
$81$	−1.64555	+	8.84829i	−0.182839	+	0.983143i
$82$	−1.78443			−0.197057
$83$	3.47650	+	6.02148i	0.381596	+	0.660943i	0.991291	−	0.131693i	$-0.0420414\pi$
$83$	3.47650	+	6.02148i	0.381596	+	0.660943i	−0.609695	+	0.792636i	$0.708708\pi$
$84$	0.442113	+	0.207419i	0.0482384	+	0.0226312i
$85$	−1.35931	+	2.35439i	−0.147437	+	0.255369i
$86$	3.25808	−	5.64316i	0.351328	−	0.608518i
$87$	−1.02536	−	12.0438i	−0.109930	−	1.29123i
$88$		0			0
$89$	12.4803			1.32291			0.661453	−	0.749986i	$-0.269940\pi$
$89$	12.4803			1.32291			0.661453	+	0.749986i	$0.269940\pi$
$90$	1.75531	+	2.11185i	0.185026	+	0.222608i
$91$	−1.13705			−0.119195
$92$	0.869338	+	1.50574i	0.0906347	+	0.156984i
$93$	12.9724	−	9.03831i	1.34518	−	0.937229i
$94$	0.175916	−	0.304695i	0.0181443	−	0.0314269i
$95$	−0.742586	+	1.28620i	−0.0761877	+	0.131961i
$96$	3.09733	−	2.15801i	0.316120	−	0.220251i
$97$	−7.09023	−	12.2806i	−0.719904	−	1.24691i	−0.961037	−	0.276419i	$-0.910852\pi$
$97$	−7.09023	−	12.2806i	−0.719904	−	1.24691i	0.241133	−	0.970492i	$-0.422481\pi$
$98$	−10.0171			−1.01188
$99$		0			0
$100$	−1.81581			−0.181581
$101$	7.18427	+	12.4435i	0.714861	+	1.23818i	0.963013	+	0.269455i	$0.0868436\pi$
$101$	7.18427	+	12.4435i	0.714861	+	1.23818i	−0.248151	+	0.968721i	$0.579823\pi$
$102$	−1.04317	−	12.2530i	−0.103289	−	1.21323i
$103$	2.21443	−	3.83550i	0.218194	−	0.377923i	−0.736062	−	0.676914i	$-0.763317\pi$
$103$	2.21443	−	3.83550i	0.218194	−	0.377923i	0.954256	+	0.298991i	$0.0966501\pi$
$104$	−1.95961	+	3.39414i	−0.192155	+	0.332823i
$105$	0.670216	+	0.314434i	0.0654064	+	0.0306856i
$106$	4.40927	+	7.63708i	0.428266	+	0.741778i
$107$	−15.7444			−1.52207			−0.761035	−	0.648711i	$-0.775308\pi$
$107$	−15.7444			−1.52207			−0.761035	+	0.648711i	$0.775308\pi$
$108$	−1.95642	−	0.538939i	−0.188257	−	0.0518594i
$109$	−13.6970			−1.31194			−0.655969	−	0.754788i	$-0.727740\pi$
$109$	−13.6970			−1.31194			−0.655969	+	0.754788i	$0.727740\pi$
$110$		0			0
$111$	4.53435	+	2.12731i	0.430381	+	0.201915i
$112$	1.67079	−	2.89390i	0.157875	−	0.273448i
$113$	−4.01507	+	6.95430i	−0.377706	+	0.654205i	−0.990728	−	0.135860i	$-0.956620\pi$
$113$	−4.01507	+	6.95430i	−0.377706	+	0.654205i	0.613022	+	0.790066i	$0.289954\pi$
$114$	−0.569883	−	6.69378i	−0.0533744	−	0.626930i
$115$	1.31786	+	2.28261i	0.122891	+	0.212854i
$116$	2.72542			0.253049
$117$	4.65689	−	0.798729i	0.430530	−	0.0738425i
$118$	11.0294			1.01534
$119$	−1.65760	−	2.87105i	−0.151952	−	0.263188i
$120$	2.09367	−	1.45873i	0.191125	−	0.133163i
$121$		0			0
$122$	−3.52438	+	6.10441i	−0.319083	+	0.552668i
$123$	1.64015	−	1.14275i	0.147888	−	0.103038i
$124$	1.78246	+	3.08732i	0.160070	+	0.277249i
$125$	−5.71281			−0.510969
$126$	−3.30051	+	0.566088i	−0.294033	+	0.0504311i
$127$	−11.9963			−1.06450			−0.532250	−	0.846587i	$-0.678653\pi$
$127$	−11.9963			−1.06450			−0.532250	+	0.846587i	$0.678653\pi$
$128$	−6.73079	−	11.6581i	−0.594924	−	1.03044i
$129$	0.619227	+	7.27338i	0.0545199	+	0.640386i
$130$	0.720832	−	1.24852i	0.0632211	−	0.109502i
$131$	3.44555	−	5.96786i	0.301039	−	0.521414i	−0.675333	−	0.737513i	$-0.736000\pi$
$131$	3.44555	−	5.96786i	0.301039	−	0.521414i	0.976372	+	0.216099i	$0.0693333\pi$
$132$		0			0
$133$	−0.905543	−	1.56845i	−0.0785205	−	0.136002i
$134$	−12.5104			−1.08074
$135$	−2.96582	−	0.816999i	−0.255257	−	0.0703161i
$136$	−11.4270			−0.979854
$137$	−4.62327	−	8.00775i	−0.394993	−	0.684148i	0.598107	−	0.801416i	$-0.295920\pi$
$137$	−4.62327	−	8.00775i	−0.394993	−	0.684148i	−0.993100	+	0.117268i	$0.962586\pi$
$138$	−10.7936	−	5.06384i	−0.918809	−	0.431063i
$139$	−10.8056	+	18.7159i	−0.916523	+	1.58746i	−0.111867	+	0.993723i	$0.535683\pi$
$139$	−10.8056	+	18.7159i	−0.916523	+	1.58746i	−0.804656	+	0.593741i	$0.797650\pi$
$140$	−0.0834615	+	0.144559i	−0.00705378	+	0.0122175i
$141$	0.0334344	+	0.392717i	0.00281568	+	0.0330727i
$142$	9.51601	+	16.4822i	0.798566	+	1.38316i
$143$		0			0
$144$	−4.81007	+	13.0259i	−0.400839	+	1.08549i
$145$	4.13157			0.343108
$146$	−11.9697	−	20.7321i	−0.990617	−	1.71580i
$147$	9.20719	−	6.41496i	0.759396	−	0.529097i
$148$	−0.564659	+	0.978018i	−0.0464147	+	0.0803926i
$149$	0.573216	−	0.992840i	0.0469597	−	0.0813366i	−0.841590	−	0.540117i	$-0.818380\pi$
$149$	0.573216	−	0.992840i	0.0469597	−	0.0813366i	0.888550	+	0.458780i	$0.151713\pi$
$150$	10.2162	−	7.11793i	0.834145	−	0.581177i
$151$	−0.440320	−	0.762657i	−0.0358327	−	0.0620641i	0.847553	−	0.530711i	$-0.178075\pi$
$151$	−0.440320	−	0.762657i	−0.0358327	−	0.0620641i	−0.883386	+	0.468647i	$0.844742\pi$
$152$	−6.24252			−0.506335
$153$	8.80566	+	10.5943i	0.711896	+	0.856496i
$154$		0			0
$155$	2.70211	+	4.68018i	0.217038	+	0.375921i
$156$	0.0903733	+	1.06152i	0.00723566	+	0.0849893i
$157$	4.89311	−	8.47511i	0.390512	−	0.676387i	−0.602005	−	0.798493i	$-0.705631\pi$
$157$	4.89311	−	8.47511i	0.390512	−	0.676387i	0.992517	+	0.122105i	$0.0389645\pi$
$158$	11.3019	−	19.5755i	0.899132	−	1.55734i
$159$	−8.94356	−	4.19591i	−0.709271	−	0.332757i
$160$	0.645162	+	1.11745i	0.0510045	+	0.0883425i
$161$	−3.21412			−0.253308
$162$	13.1199	−	4.63694i	1.03080	−	0.364313i
$163$	4.62976			0.362631			0.181315	−	0.983425i	$-0.441965\pi$
$163$	4.62976			0.362631			0.181315	+	0.983425i	$0.441965\pi$
$164$	0.225364	+	0.390342i	0.0175980	+	0.0304806i
$165$		0			0
$166$	5.37515	−	9.31002i	0.417192	−	0.722598i
$167$	8.49369	−	14.7115i	0.657262	−	1.13841i	−0.324060	−	0.946036i	$-0.605048\pi$
$167$	8.49369	−	14.7115i	0.657262	−	1.13841i	0.981322	−	0.192374i	$-0.0616186\pi$
$168$	0.263962	+	3.10048i	0.0203651	+	0.239207i
$169$	5.25974	+	9.11014i	0.404596	+	0.700780i
$170$	4.20335			0.322382
$171$	4.81051	+	5.78763i	0.367869	+	0.442591i
$172$	−1.64592			−0.125500
$173$	0.295528	+	0.511869i	0.0224686	+	0.0389167i	0.877041	−	0.480415i	$-0.159514\pi$
$173$	0.295528	+	0.511869i	0.0224686	+	0.0389167i	−0.854572	+	0.519332i	$0.826181\pi$
$174$	−15.3338	+	10.6836i	−1.16246	+	0.809921i
$175$	1.67835	−	2.90699i	0.126872	−	0.219748i
$176$		0			0
$177$	−10.1377	+	7.06327i	−0.761996	+	0.530908i
$178$	−9.64811	−	16.7110i	−0.723156	−	1.25254i
$179$	−9.64093			−0.720597			−0.360298	−	0.932837i	$-0.617325\pi$
$179$	−9.64093			−0.720597			−0.360298	+	0.932837i	$0.617325\pi$
$180$	0.240278	−	0.650687i	0.0179093	−	0.0484993i
$181$	−4.76187			−0.353947			−0.176973	−	0.984216i	$-0.556631\pi$
$181$	−4.76187			−0.353947			−0.176973	+	0.984216i	$0.556631\pi$
$182$	0.879014	+	1.52250i	0.0651569	+	0.112855i
$183$	−0.669841	−	7.86788i	−0.0495161	−	0.581611i
$184$	−5.53928	+	9.59432i	−0.408361	+	0.707303i
$185$	−0.855988	+	1.48262i	−0.0629335	+	0.109004i
$186$	−22.1308	−	10.3827i	−1.62271	−	0.761300i
$187$		0			0
$188$	−0.0888691			−0.00648144
$189$	2.67113	−	2.63397i	0.194296	−	0.191593i
$190$	2.29628			0.166590
$191$	2.59901	+	4.50162i	0.188058	+	0.325726i	0.944603	−	0.328216i	$-0.106447\pi$
$191$	2.59901	+	4.50162i	0.188058	+	0.325726i	−0.756545	+	0.653942i	$0.773114\pi$
$192$	9.23168	+	4.33108i	0.666239	+	0.312568i
$193$	−1.63402	+	2.83021i	−0.117620	+	0.203723i	−0.918824	−	0.394668i	$-0.870860\pi$
$193$	−1.63402	+	2.83021i	−0.117620	+	0.203723i	0.801204	+	0.598391i	$0.204193\pi$
$194$	−10.9625	+	18.9876i	−0.787060	+	1.36323i
$195$	0.137000	+	1.60919i	0.00981081	+	0.115237i
$196$	1.26511	+	2.19123i	0.0903648	+	0.156516i
$197$	−22.4626			−1.60039			−0.800197	−	0.599737i	$-0.795272\pi$
$197$	−22.4626			−1.60039			−0.800197	+	0.599737i	$0.795272\pi$
$198$		0			0
$199$	−20.8291			−1.47654			−0.738269	−	0.674507i	$-0.764356\pi$
$199$	−20.8291			−1.47654			−0.738269	+	0.674507i	$0.764356\pi$
$200$	−5.78502	−	10.0199i	−0.409062	−	0.708517i
$201$	11.4990	−	8.01170i	0.811074	−	0.565102i
$202$	11.1079	−	19.2394i	0.781546	−	1.35368i
$203$	−2.51911	+	4.36323i	−0.176807	+	0.306238i
$204$	−2.54858	+	1.77568i	−0.178437	+	0.124323i
$205$	0.341638	+	0.591734i	0.0238610	+	0.0413285i
$206$	−6.84761			−0.477096
$207$	13.1638	−	2.25779i	0.914946	−	0.156927i
$208$	7.28981			0.505457
$209$		0			0
$210$	−0.0970972	−	1.14049i	−0.00670034	−	0.0787015i
$211$	−1.69601	+	2.93758i	−0.116758	+	0.202231i	−0.918481	−	0.395465i	$-0.870584\pi$
$211$	−1.69601	+	2.93758i	−0.116758	+	0.202231i	0.801723	+	0.597696i	$0.203917\pi$
$212$	1.11374	−	1.92905i	0.0764917	−	0.132487i
$213$	−19.3019	−	9.05553i	−1.32254	−	0.620475i
$214$	12.1715	+	21.0817i	0.832027	+	1.44111i
$215$	−2.49511			−0.170165
$216$	−3.25904	−	12.5129i	−0.221750	−	0.851395i
$217$	−6.59014			−0.447368
$218$	10.5887	+	18.3402i	0.717160	+	1.24216i
$219$	24.2787	+	11.3905i	1.64061	+	0.769696i
$220$		0			0
$221$	3.61612	−	6.26330i	0.243247	−	0.421315i
$222$	−0.656911	−	7.71601i	−0.0440890	−	0.517865i
$223$	5.51320	+	9.54913i	0.369191	+	0.639457i	0.989439	−	0.144948i	$-0.0463015\pi$
$223$	5.51320	+	9.54913i	0.369191	+	0.639457i	−0.620248	+	0.784405i	$0.712968\pi$
$224$	−1.57348			−0.105133
$225$	−4.83183	+	13.0849i	−0.322122	+	0.872325i
$226$	12.4157			0.825879
$227$	2.98344	+	5.16748i	0.198018	+	0.342978i	0.947886	−	0.318610i	$-0.103216\pi$
$227$	2.98344	+	5.16748i	0.198018	+	0.342978i	−0.749868	+	0.661588i	$0.769883\pi$
$228$	−1.39229	+	0.970052i	−0.0922064	+	0.0642432i
$229$	−12.3753	+	21.4347i	−0.817785	+	1.41645i	0.0895253	+	0.995985i	$0.471465\pi$
$229$	−12.3753	+	21.4347i	−0.817785	+	1.41645i	−0.907311	+	0.420461i	$0.861868\pi$
$230$	2.03760	−	3.52922i	0.134355	−	0.232710i
$231$		0			0
$232$	8.68297	+	15.0393i	0.570065	+	0.987381i
$233$	4.18842			0.274392			0.137196	−	0.990544i	$-0.456191\pi$
$233$	4.18842			0.274392			0.137196	+	0.990544i	$0.456191\pi$
$234$	−4.66959	−	5.61808i	−0.305261	−	0.367265i
$235$	−0.134720			−0.00878817
$236$	−1.39296	−	2.41268i	−0.0906741	−	0.157052i
$237$	2.14803	+	25.2305i	0.139530	+	1.63890i
$238$	−2.56287	+	4.43903i	−0.166126	+	0.287740i
$239$	3.68642	−	6.38507i	0.238455	−	0.413016i	−0.721816	−	0.692085i	$-0.756692\pi$
$239$	3.68642	−	6.38507i	0.238455	−	0.413016i	0.960271	+	0.279069i	$0.0900258\pi$
$240$	−4.29687	−	2.01589i	−0.277362	−	0.130125i
$241$	4.41462	+	7.64634i	0.284371	+	0.492544i	0.972456	−	0.233085i	$-0.0748821\pi$
$241$	4.41462	+	7.64634i	0.284371	+	0.492544i	−0.688086	+	0.725629i	$0.741549\pi$
$242$		0			0
$243$	−9.08965	+	12.6641i	−0.583101	+	0.812399i
$244$	1.78045			0.113981
$245$	1.91782	+	3.32177i	0.122525	+	0.212220i
$246$	−2.79808	−	1.31273i	−0.178399	−	0.0836967i
$247$	1.97548	−	3.42163i	0.125697	−	0.217713i
$248$	−11.3576	+	19.6719i	−0.721207	+	1.24917i
$249$	1.02159	+	11.9995i	0.0647409	+	0.760440i
$250$	4.41639	+	7.64942i	0.279317	+	0.483792i
$251$	20.5731			1.29856			0.649280	−	0.760550i	$-0.275070\pi$
$251$	20.5731			1.29856			0.649280	+	0.760550i	$0.275070\pi$
$252$	0.540668	+	0.650489i	0.0340589	+	0.0409770i
$253$		0			0
$254$	9.27397	+	16.0630i	0.581901	+	1.00788i
$255$	−3.86350	+	2.69183i	−0.241942	+	0.168569i
$256$	−4.51939	+	7.82782i	−0.282462	+	0.489239i
$257$	1.69119	−	2.92923i	0.105494	−	0.182721i	−0.808446	−	0.588570i	$-0.799691\pi$
$257$	1.69119	−	2.92923i	0.105494	−	0.182721i	0.913940	+	0.405850i	$0.133024\pi$
$258$	9.26031	−	6.45196i	0.576522	−	0.401682i
$259$	−1.04383	−	1.80797i	−0.0648605	−	0.112342i
$260$	−0.364149			−0.0225836
$261$	7.25229	−	19.6396i	0.448905	−	1.21566i
$262$	−10.6546			−0.658241
$263$	7.14112	+	12.3688i	0.440341	+	0.762692i	0.997715	−	0.0675692i	$-0.0215244\pi$
$263$	7.14112	+	12.3688i	0.440341	+	0.762692i	−0.557374	+	0.830262i	$0.688191\pi$
$264$		0			0
$265$	1.68836	−	2.92432i	0.103715	−	0.179639i
$266$	−1.40009	+	2.42503i	−0.0858452	+	0.148688i
$267$	19.5698	+	9.18124i	1.19765	+	0.561883i
$268$	1.58000	+	2.73665i	0.0965141	+	0.167167i
$269$	6.72041			0.409751			0.204875	−	0.978788i	$-0.434321\pi$
$269$	6.72041			0.409751			0.204875	+	0.978788i	$0.434321\pi$
$270$	1.19882	+	4.60280i	0.0729580	+	0.280118i
$271$	−3.98035			−0.241789			−0.120895	−	0.992665i	$-0.538576\pi$
$271$	−3.98035			−0.241789			−0.120895	+	0.992665i	$0.538576\pi$
$272$	10.6272	+	18.4068i	0.644367	+	1.11608i
$273$	−1.78295	−	0.836480i	−0.107909	−	0.0506260i
$274$	−7.14821	+	12.3811i	−0.431839	+	0.747968i
$275$		0			0
$276$	0.255461	+	3.00062i	0.0153769	+	0.180616i
$277$	6.56600	+	11.3726i	0.394513	+	0.683316i	0.993039	−	0.117787i	$-0.0375800\pi$
$277$	6.56600	+	11.3726i	0.394513	+	0.683316i	−0.598526	+	0.801103i	$0.704247\pi$
$278$	33.4140			2.00404
$279$	26.9906	−	4.62930i	1.61589	−	0.277149i
$280$	−1.06361			−0.0635627
$281$	1.48393	+	2.57025i	0.0885241	+	0.153328i	0.906887	−	0.421373i	$-0.138452\pi$
$281$	1.48393	+	2.57025i	0.0885241	+	0.153328i	−0.818363	+	0.574701i	$0.805118\pi$
$282$	0.499998	−	0.348365i	0.0297745	−	0.0207449i
$283$	−4.04639	+	7.00855i	−0.240533	+	0.416615i	−0.960866	−	0.277013i	$-0.910655\pi$
$283$	−4.04639	+	7.00855i	−0.240533	+	0.416615i	0.720333	+	0.693628i	$0.243989\pi$
$284$	2.40365	−	4.16324i	0.142630	−	0.247043i
$285$	−2.11062	+	1.47054i	−0.125022	+	0.0871072i
$286$		0			0
$287$	−0.833217			−0.0491833
$288$	6.44435	−	1.10531i	0.379737	−	0.0651307i
$289$	4.08649			0.240382
$290$	−3.19398	−	5.53214i	−0.187557	−	0.324859i
$291$	−2.08352	−	24.4728i	−0.122138	−	1.43462i
$292$	−3.02341	+	5.23671i	−0.176932	+	0.306455i
$293$	7.85779	−	13.6101i	0.459057	−	0.795110i	−0.539854	−	0.841758i	$-0.681521\pi$
$293$	7.85779	−	13.6101i	0.459057	−	0.795110i	0.998911	+	0.0466485i	$0.0148541\pi$
$294$	−15.7074	−	7.36917i	−0.916073	−	0.429779i
$295$	−2.11165	−	3.65748i	−0.122945	−	0.212947i
$296$	−7.19584			−0.418249
$297$		0			0
$298$	−1.77254			−0.102681
$299$	−3.50587	−	6.07235i	−0.202750	−	0.351173i
$300$	−2.84729	−	1.33582i	−0.164388	−	0.0771234i
$301$	1.52132	−	2.63501i	0.0876876	−	0.151879i
$302$	−0.680795	+	1.17917i	−0.0391754	+	0.0678537i
$303$	2.11115	+	24.7973i	0.121282	+	1.42457i
$304$	5.80560	+	10.0556i	0.332974	+	0.576728i
$305$	2.69905			0.154547
$306$	7.37829	−	19.9808i	0.421788	−	1.14223i
$307$	−3.51315			−0.200506			−0.100253	−	0.994962i	$-0.531965\pi$
$307$	−3.51315			−0.200506			−0.100253	+	0.994962i	$0.531965\pi$
$308$		0			0
$309$	6.29397	−	4.38522i	0.358051	−	0.249466i
$310$	4.17782	−	7.23620i	0.237284	−	0.410989i
$311$	−13.1672	+	22.8063i	−0.746644	+	1.29323i	0.202779	+	0.979225i	$0.435003\pi$
$311$	−13.1672	+	22.8063i	−0.746644	+	1.29323i	−0.949423	+	0.314001i	$0.898331\pi$
$312$	−5.56971	+	3.88060i	−0.315323	+	0.219696i
$313$	1.23057	+	2.13141i	0.0695560	+	0.120474i	0.898706	−	0.438552i	$-0.144508\pi$
$313$	1.23057	+	2.13141i	0.0695560	+	0.120474i	−0.829150	+	0.559026i	$0.811175\pi$
$314$	−15.1308			−0.853882
$315$	0.819620	+	0.986102i	0.0461804	+	0.0555605i
$316$	−5.70949			−0.321184
$317$	13.2536	+	22.9559i	0.744395	+	1.28933i	0.950477	+	0.310795i	$0.100595\pi$
$317$	13.2536	+	22.9559i	0.744395	+	1.28933i	−0.206082	+	0.978535i	$0.566071\pi$
$318$	1.29569	+	15.2191i	0.0726589	+	0.853444i
$319$		0			0
$320$	−1.74274	+	3.01852i	−0.0974224	+	0.168741i
$321$	−24.6881	−	11.5825i	−1.37796	−	0.646474i
$322$	2.48474	+	4.30369i	0.138469	+	0.239835i
$323$	11.5195			0.640962
$324$	−2.67131	−	2.28435i	−0.148406	−	0.126908i
$325$	7.32279			0.406196
$326$	−3.57912	−	6.19922i	−0.198229	−	0.343343i
$327$	−21.4777	−	10.0764i	−1.18772	−	0.557224i
$328$	−1.43598	+	2.48720i	−0.0792889	+	0.137332i
$329$	0.0821419	−	0.142274i	0.00452863	−	0.00784382i
$330$		0			0
$331$	−4.05198	−	7.01824i	−0.222717	−	0.385757i	0.732915	−	0.680320i	$-0.238159\pi$
$331$	−4.05198	−	7.01824i	−0.222717	−	0.385757i	−0.955632	+	0.294563i	$0.904826\pi$
$332$	−2.71541			−0.149028
$333$	5.54514	+	6.67147i	0.303872	+	0.365595i
$334$	−26.2648			−1.43715
$335$	2.39519	+	4.14859i	0.130863	+	0.226662i
$336$	4.74883	−	3.30867i	0.259070	−	0.180503i
$337$	−12.3603	+	21.4087i	−0.673309	+	1.16621i	0.303651	+	0.952783i	$0.401794\pi$
$337$	−12.3603	+	21.4087i	−0.673309	+	1.16621i	−0.976960	+	0.213423i	$0.931539\pi$
$338$	8.13228	−	14.0855i	0.442338	−	0.766152i
$339$	−11.4119	+	7.95102i	−0.619807	+	0.431840i
$340$	−0.530861	−	0.919478i	−0.0287900	−	0.0498657i
$341$		0			0
$342$	4.03074	−	10.9155i	0.217957	−	0.590241i
$343$	−9.73102			−0.525426
$344$	−5.24376	−	9.08245i	−0.282724	−	0.489693i
$345$	0.387263	+	4.54876i	0.0208496	+	0.244897i
$346$	0.456926	−	0.791420i	0.0245645	−	0.0425470i
$347$	1.03482	−	1.79236i	0.0555522	−	0.0962192i	−0.836912	−	0.547337i	$-0.815641\pi$
$347$	1.03482	−	1.79236i	0.0555522	−	0.0962192i	0.892464	+	0.451118i	$0.148975\pi$
$348$	4.27361	+	2.00498i	0.229090	+	0.107478i
$349$	2.60713	+	4.51569i	0.139557	+	0.241719i	0.927329	−	0.374247i	$-0.122099\pi$
$349$	2.60713	+	4.51569i	0.139557	+	0.241719i	−0.787772	+	0.615967i	$0.788766\pi$
$350$	−5.18993			−0.277413
$351$	7.88987	+	2.17344i	0.421130	+	0.116009i
$352$		0			0
$353$	−10.8363	−	18.7689i	−0.576756	−	0.998970i	−0.995848	−	0.0910266i	$-0.970985\pi$
$353$	−10.8363	−	18.7689i	−0.576756	−	0.998970i	0.419093	−	0.907943i	$-0.362348\pi$
$354$	17.2948	+	8.11392i	0.919209	+	0.431250i
$355$	3.64378	−	6.31121i	0.193392	−	0.334964i
$356$	−2.43701	+	4.22103i	−0.129161	+	0.223714i
$357$	−0.487097	−	5.72139i	−0.0257799	−	0.302808i
$358$	7.45310	+	12.9091i	0.393908	+	0.682269i
$359$	8.75285			0.461958			0.230979	−	0.972959i	$-0.425807\pi$
$359$	8.75285			0.461958			0.230979	+	0.972959i	$0.425807\pi$
$360$	4.35611	−	0.747140i	0.229587	−	0.0393778i
$361$	−12.7069			−0.668786
$362$	3.68125	+	6.37611i	0.193482	+	0.335121i
$363$		0			0
$364$	0.222030	−	0.384567i	0.0116375	−	0.0201568i
$365$	−4.58331	+	7.93853i	−0.239902	+	0.415522i
$366$	−10.0172	+	6.97932i	−0.523608	+	0.364815i
$367$	3.38311	+	5.85972i	0.176597	+	0.305875i	0.940713	−	0.339204i	$-0.110158\pi$
$367$	3.38311	+	5.85972i	0.176597	+	0.305875i	−0.764116	+	0.645079i	$0.776824\pi$
$368$	20.6063			1.07418
$369$	3.41253	−	0.585301i	0.177649	−	0.0304696i
$370$	2.64695			0.137608
$371$	2.05886	+	3.56604i	0.106890	+	0.185140i
$372$	0.523789	+	6.15238i	0.0271572	+	0.318986i
$373$	10.9467	−	18.9602i	0.566797	−	0.981722i	−0.430083	−	0.902790i	$-0.641516\pi$
$373$	10.9467	−	18.9602i	0.566797	−	0.981722i	0.996880	−	0.0789323i	$-0.0251511\pi$
$374$		0			0
$375$	−8.95802	−	4.20269i	−0.462590	−	0.217026i
$376$	−0.283130	−	0.490395i	−0.0146013	−	0.0252902i
$377$	−10.9911			−0.566069
$378$	−5.59183	−	1.54039i	−0.287613	−	0.0792293i
$379$	−33.8236			−1.73740			−0.868701	−	0.495337i	$-0.835045\pi$
$379$	−33.8236			−1.73740			−0.868701	+	0.495337i	$0.835045\pi$
$380$	−0.290008	−	0.502309i	−0.0148771	−	0.0257679i
$381$	−18.8109	−	8.82521i	−0.963712	−	0.452129i
$382$	4.01843	−	6.96012i	0.205601	−	0.356111i
$383$	9.18694	−	15.9123i	0.469431	−	0.813078i	−0.529958	−	0.848024i	$-0.677792\pi$
$383$	9.18694	−	15.9123i	0.469431	−	0.813078i	0.999389	+	0.0349456i	$0.0111258\pi$
$384$	−1.97789	−	23.2321i	−0.100934	−	1.18556i
$385$		0			0
$386$	5.05284			0.257183
$387$	−4.37975	+	11.8606i	−0.222635	+	0.602909i
$388$	5.53801			0.281150
$389$	15.4033	+	26.6792i	0.780977	+	1.35269i	0.931373	+	0.364066i	$0.118612\pi$
$389$	15.4033	+	26.6792i	0.780977	+	1.35269i	−0.150396	+	0.988626i	$0.548055\pi$
$390$	2.04879	−	1.42746i	0.103744	−	0.0722822i
$391$	10.2218	−	17.7047i	0.516938	−	0.895364i
$392$	−8.06106	+	13.9622i	−0.407145	+	0.705196i
$393$	9.79313	−	6.82320i	0.493998	−	0.344185i
$394$	17.3651	+	30.0773i	0.874842	+	1.51527i
$395$	−8.65524			−0.435493
$396$		0			0
$397$	−8.29578			−0.416353			−0.208177	−	0.978091i	$-0.566753\pi$
$397$	−8.29578			−0.416353			−0.208177	+	0.978091i	$0.566753\pi$
$398$	16.1023	+	27.8901i	0.807137	+	1.39800i
$399$	−0.266100	−	3.12558i	−0.0133217	−	0.156475i
$400$	−10.7602	+	18.6373i	−0.538012	+	0.931863i
$401$	1.96681	−	3.40662i	0.0982179	−	0.170118i	−0.812729	−	0.582642i	$-0.802019\pi$
$401$	1.96681	−	3.40662i	0.0982179	−	0.170118i	0.910947	+	0.412523i	$0.135352\pi$
$402$	−19.6171	−	9.20343i	−0.978412	−	0.459025i
$403$	−7.18833	−	12.4505i	−0.358076	−	0.620206i
$404$	−5.61146			−0.279181
$405$	−4.04954	−	3.46293i	−0.201223	−	0.172075i
$406$	7.78977			0.386600
$407$		0			0
$408$	−17.9181	−	8.40636i	−0.887080	−	0.416177i
$409$	1.25213	−	2.16875i	0.0619137	−	0.107238i	−0.833407	−	0.552660i	$-0.813613\pi$
$409$	1.25213	−	2.16875i	0.0619137	−	0.107238i	0.895321	+	0.445422i	$0.146946\pi$
$410$	0.528219	−	0.914902i	0.0260869	−	0.0451838i
$411$	−1.35858	−	15.9578i	−0.0670139	−	0.787138i
$412$	0.864818	+	1.49791i	0.0426065	+	0.0737966i
$413$	5.15007			0.253418
$414$	−13.1997	−	15.8808i	−0.648728	−	0.780498i
$415$	−4.11640			−0.202066
$416$	−1.71630	−	2.97273i	−0.0841488	−	0.145750i
$417$	−30.7124	+	21.3984i	−1.50399	+	1.04788i
$418$		0			0
$419$	−5.36970	+	9.30060i	−0.262327	+	0.454364i	−0.966860	−	0.255307i	$-0.917823\pi$
$419$	−5.36970	+	9.30060i	−0.262327	+	0.454364i	0.704533	+	0.709672i	$0.251157\pi$
$420$	−0.237219	+	0.165278i	−0.0115751	+	0.00806476i
$421$	−11.0937	−	19.2149i	−0.540675	−	0.936477i	−0.998865	−	0.0476226i	$-0.984836\pi$
$421$	−11.0937	−	19.2149i	−0.540675	−	0.936477i	0.458190	−	0.888854i	$-0.348498\pi$
$422$	5.24453			0.255300
$423$	−0.236479	+	0.640399i	−0.0114980	+	0.0311373i
$424$	14.1931			0.689278
$425$	10.6753	+	18.4901i	0.517826	+	0.896901i
$426$	2.79635	+	32.8456i	0.135483	+	1.59137i
$427$	−1.64567	+	2.85039i	−0.0796396	+	0.137940i
$428$	3.07440	−	5.32501i	0.148606	−	0.257394i
$429$		0			0
$430$	1.92889	+	3.34093i	0.0930192	+	0.161114i
$431$	−18.4582			−0.889100			−0.444550	−	0.895754i	$-0.646636\pi$
$431$	−18.4582			−0.889100			−0.444550	+	0.895754i	$0.646636\pi$
$432$	−17.1251	+	16.8868i	−0.823933	+	0.812469i
$433$	15.1166			0.726459			0.363230	−	0.931700i	$-0.381674\pi$
$433$	15.1166			0.726459			0.363230	+	0.931700i	$0.381674\pi$
$434$	5.09463	+	8.82415i	0.244550	+	0.423573i
$435$	6.47853	+	3.03943i	0.310622	+	0.145729i
$436$	2.67461	−	4.63255i	0.128090	−	0.221859i
$437$	5.58414	−	9.67202i	0.267126	−	0.462675i
$438$	−3.51737	−	41.3147i	−0.168066	−	1.97409i
$439$	−11.9777	−	20.7459i	−0.571663	−	0.990150i	−0.996395	−	0.0848306i	$-0.972965\pi$
$439$	−11.9777	−	20.7459i	−0.571663	−	0.990150i	0.424732	−	0.905319i	$-0.360368\pi$
$440$		0			0
$441$	19.1566	−	3.28566i	0.912221	−	0.156460i
$442$	−11.1820			−0.531875
$443$	−12.7489	−	22.0817i	−0.605716	−	1.04913i	−0.991938	−	0.126725i	$-0.959553\pi$
$443$	−12.7489	−	22.0817i	−0.605716	−	1.04913i	0.386222	−	0.922406i	$-0.373780\pi$
$444$	−1.60491	+	1.11819i	−0.0761655	+	0.0530670i
$445$	−3.69436	+	6.39882i	−0.175130	+	0.303333i
$446$	8.52415	−	14.7643i	0.403630	−	0.699108i
$447$	1.62923	−	1.13514i	0.0770599	−	0.0536902i
$448$	−2.12518	−	3.68092i	−0.100405	−	0.173907i
$449$	−22.4824			−1.06101			−0.530505	−	0.847682i	$-0.677998\pi$
$449$	−22.4824			−1.06101			−0.530505	+	0.847682i	$0.677998\pi$
$450$	21.2559	−	3.64571i	1.00201	−	0.171861i
$451$		0			0
$452$	−1.56804	−	2.71592i	−0.0737542	−	0.127746i
$453$	−0.129391	−	1.51982i	−0.00607933	−	0.0714072i
$454$	4.61281	−	7.98963i	0.216490	−	0.374972i
$455$	0.336584	−	0.582980i	0.0157793	−	0.0273305i
$456$	−9.78863	−	4.59237i	−0.458395	−	0.215058i
$457$	−10.8448	−	18.7837i	−0.507298	−	0.878666i	−0.999964	−	0.00844735i	$-0.997311\pi$
$457$	−10.8448	−	18.7837i	−0.507298	−	0.878666i	0.492667	−	0.870218i	$-0.336022\pi$
$458$	38.2679			1.78814
$459$	6.01400	+	23.0904i	0.280710	+	1.07777i
$460$	−1.02935			−0.0479938
$461$	6.05182	+	10.4821i	0.281861	+	0.488198i	0.971843	−	0.235629i	$-0.0757149\pi$
$461$	6.05182	+	10.4821i	0.281861	+	0.488198i	−0.689982	+	0.723827i	$0.742382\pi$
$462$		0			0
$463$	−10.0154	+	17.3472i	−0.465455	+	0.806192i	−0.999222	−	0.0394398i	$-0.987443\pi$
$463$	−10.0154	+	17.3472i	−0.465455	+	0.806192i	0.533767	+	0.845632i	$0.320776\pi$
$464$	16.1505	−	27.9734i	0.749767	−	1.29863i
$465$	0.794033	+	9.32663i	0.0368224	+	0.432512i
$466$	−3.23793	−	5.60826i	−0.149994	−	0.259798i
$467$	6.06750			0.280770			0.140385	−	0.990097i	$-0.455166\pi$
$467$	6.06750			0.280770			0.140385	+	0.990097i	$0.455166\pi$
$468$	−0.639204	+	1.73100i	−0.0295472	+	0.0800156i
$469$	−5.84161			−0.269740
$470$	0.104148	+	0.180389i	0.00480398	+	0.00832074i
$471$	13.9075	−	9.68980i	0.640822	−	0.446482i
$472$	8.87574	−	15.3732i	0.408539	−	0.707610i
$473$		0			0
$474$	32.1230	−	22.3811i	1.47546	−	1.02800i
$475$	5.83187	+	10.1011i	0.267584	+	0.463470i
$476$	1.29471			0.0593430
$477$	−10.9373	−	13.1588i	−0.500783	−	0.602502i
$478$	−11.3994			−0.521397
$479$	−18.1364	−	31.4132i	−0.828673	−	1.43530i	−0.899079	−	0.437786i	$-0.855763\pi$
$479$	−18.1364	−	31.4132i	−0.828673	−	1.43530i	0.0704058	−	0.997518i	$-0.477571\pi$
$480$	0.189585	+	2.22685i	0.00865335	+	0.101641i
$481$	2.27716	−	3.94416i	0.103830	−	0.179838i
$482$	6.82560	−	11.8223i	0.310898	−	0.538491i
$483$	−5.03993	−	2.36450i	−0.229325	−	0.107589i
$484$		0			0
$485$	8.39529			0.381211
$486$	23.9840	+	2.38081i	1.08794	+	0.107996i
$487$	−8.68493			−0.393552			−0.196776	−	0.980449i	$-0.563047\pi$
$487$	−8.68493			−0.393552			−0.196776	+	0.980449i	$0.563047\pi$
$488$	5.67236	+	9.82482i	0.256776	+	0.444749i
$489$	7.25973	+	3.40593i	0.328296	+	0.154021i
$490$	2.96522	−	5.13591i	0.133955	−	0.232017i
$491$	16.5987	−	28.7497i	0.749087	−	1.29746i	−0.199174	−	0.979964i	$-0.563826\pi$
$491$	16.5987	−	28.7497i	0.749087	−	1.29746i	0.948261	−	0.317493i	$-0.102841\pi$
$492$	0.0662247	+	0.777869i	0.00298564	+	0.0350691i
$493$	−16.0229	−	27.7525i	−0.721636	−	1.24991i
$494$	−6.10872			−0.274844
$495$		0			0
$496$	42.2506			1.89711
$497$	4.44339	+	7.69618i	0.199313	+	0.345221i
$498$	15.2775	−	10.6444i	0.684603	−	0.476986i
$499$	−10.4384	+	18.0799i	−0.467289	+	0.809368i	−0.999302	−	0.0373682i	$-0.988103\pi$
$499$	−10.4384	+	18.0799i	−0.467289	+	0.809368i	0.532013	+	0.846736i	$0.321436\pi$
$500$	1.11554	−	1.93216i	0.0498883	−	0.0864090i
$501$	24.1413	−	16.8200i	1.07855	−	0.751463i
$502$	−15.9044	−	27.5472i	−0.709847	−	1.22949i
$503$	23.3189			1.03974			0.519869	−	0.854246i	$-0.325981\pi$
$503$	23.3189			1.03974			0.519869	+	0.854246i	$0.325981\pi$
$504$	−1.86699	+	5.05591i	−0.0831622	+	0.225208i
$505$	−8.50663			−0.378540
$506$		0			0
$507$	1.54561	+	18.1546i	0.0686431	+	0.806275i
$508$	2.34251	−	4.05734i	0.103932	−	0.180016i
$509$	−3.24061	+	5.61289i	−0.143637	+	0.248787i	−0.928864	−	0.370422i	$-0.879213\pi$
$509$	−3.24061	+	5.61289i	−0.143637	+	0.248787i	0.785226	+	0.619209i	$0.212547\pi$
$510$	6.59109	+	3.09223i	0.291858	+	0.136926i
$511$	−5.58910	−	9.68060i	−0.247247	−	0.428245i
$512$	−12.9480			−0.572225
$513$	3.28544	+	12.6142i	0.145056	+	0.556932i
$514$	−5.22963			−0.230669
$515$	1.31101	+	2.27074i	0.0577701	+	0.100061i
$516$	−2.58089	−	1.21083i	−0.113617	−	0.0533040i
$517$		0			0
$518$	−1.61390	+	2.79537i	−0.0709109	+	0.122821i
$519$	0.0868429	+	1.02005i	0.00381198	+	0.0447752i
$520$	−1.16015	−	2.00944i	−0.0508760	−	0.0881198i
$521$	−33.2103			−1.45497			−0.727484	−	0.686124i	$-0.759311\pi$
$521$	−33.2103			−1.45497			−0.727484	+	0.686124i	$0.759311\pi$
$522$	−31.9038	+	5.47200i	−1.39639	+	0.239503i
$523$	−40.1386			−1.75514			−0.877569	−	0.479451i	$-0.840836\pi$
$523$	−40.1386			−1.75514			−0.877569	+	0.479451i	$0.840836\pi$
$524$	1.34562	+	2.33068i	0.0587835	+	0.101816i
$525$	4.77031	−	3.32364i	0.208194	−	0.145055i
$526$	11.0412	−	19.1238i	0.481417	−	0.833839i
$527$	20.9585	−	36.3011i	0.912965	−	1.58130i
$528$		0			0
$529$	1.58985	+	2.75370i	0.0691240	+	0.119726i
$530$	−5.22085			−0.226779
$531$	−21.0927	+	3.61772i	−0.915344	+	0.156995i
$532$	0.707298			0.0306652
$533$	−0.908849	−	1.57417i	−0.0393666	−	0.0681850i
$534$	−2.83516	−	33.3015i	−0.122690	−	1.44110i
$535$	4.66060	−	8.07239i	0.201495	−	0.349000i
$536$	−10.0675	+	17.4375i	−0.434851	+	0.753185i
$537$	−15.1175	−	7.09245i	−0.652370	−	0.306062i
$538$	−5.19534	−	8.99859i	−0.223987	−	0.387957i
$539$		0			0
$540$	0.855454	−	0.843551i	0.0368129	−	0.0363007i
$541$	24.6485			1.05972			0.529860	−	0.848085i	$-0.322244\pi$
$541$	24.6485			1.05972			0.529860	+	0.848085i	$0.322244\pi$
$542$	3.07708	+	5.32967i	0.132172	+	0.228929i
$543$	−7.46688	−	3.50312i	−0.320435	−	0.150333i
$544$	5.00410	−	8.66735i	0.214549	−	0.371610i
$545$	4.05454	−	7.02267i	0.173677	−	0.300818i
$546$	0.258305	+	3.03402i	0.0110544	+	0.129844i
$547$	−12.8602	−	22.2745i	−0.549861	−	0.952388i	−0.998284	−	0.0585660i	$-0.981347\pi$
$547$	−12.8602	−	22.2745i	−0.549861	−	0.952388i	0.448422	−	0.893822i	$-0.351986\pi$
$548$	3.61113			0.154260
$549$	4.73774	−	12.8301i	0.202202	−	0.547574i
$550$		0			0
$551$	−8.75329	−	15.1611i	−0.372902	−	0.645886i
$552$	−15.7441	+	10.9694i	−0.670112	+	0.466889i
$553$	5.27730	−	9.14055i	0.224414	−	0.388696i
$554$	10.1519	−	17.5837i	0.431314	−	0.747058i
$555$	−2.43294	+	1.69511i	−0.103273	+	0.0719534i
$556$	−4.22002	−	7.30928i	−0.178969	−	0.309983i
$557$	11.6815			0.494962			0.247481	−	0.968893i	$-0.420397\pi$
$557$	11.6815			0.494962			0.247481	+	0.968893i	$0.420397\pi$
$558$	−27.0642	−	32.5615i	−1.14572	−	1.37844i
$559$	6.63766			0.280743
$560$	0.989164	+	1.71328i	0.0417998	+	0.0723994i
$561$		0			0
$562$	2.29436	−	3.97396i	0.0967819	−	0.167631i
$563$	−4.06105	+	7.03395i	−0.171153	+	0.296445i	−0.938823	−	0.344400i	$-0.888083\pi$
$563$	−4.06105	+	7.03395i	−0.171153	+	0.296445i	0.767670	+	0.640845i	$0.221416\pi$
$564$	−0.139352	−	0.0653774i	−0.00586777	−	0.00275289i
$565$	−2.37705	−	4.11717i	−0.100003	−	0.173211i
$566$	12.5125			0.525941
$567$	6.12620	−	2.16517i	0.257276	−	0.0909285i
$568$	30.6313			1.28526
$569$	9.00331	+	15.5942i	0.377438	+	0.653742i	0.990689	−	0.136146i	$-0.0434717\pi$
$569$	9.00331	+	15.5942i	0.377438	+	0.653742i	−0.613250	+	0.789888i	$0.710138\pi$
$570$	3.60070	+	1.68928i	0.150817	+	0.0707561i
$571$	1.30322	−	2.25725i	0.0545382	−	0.0944629i	−0.837467	−	0.546487i	$-0.815965\pi$
$571$	1.30322	−	2.25725i	0.0545382	−	0.0944629i	0.892006	+	0.452024i	$0.149298\pi$
$572$		0			0
$573$	0.763738	+	8.97079i	0.0319056	+	0.374760i
$574$	0.644134	+	1.11567i	0.0268856	+	0.0465673i
$575$	20.6996			0.863231
$576$	11.2896	+	13.5827i	0.470400	+	0.565948i
$577$	35.1888			1.46493			0.732465	−	0.680805i	$-0.238370\pi$
$577$	35.1888			1.46493			0.732465	+	0.680805i	$0.238370\pi$
$578$	−3.15913	−	5.47178i	−0.131403	−	0.227596i
$579$	−4.64431	+	3.23585i	−0.193011	+	0.134477i
$580$	−0.806767	+	1.39736i	−0.0334992	+	0.0580223i
$581$	2.50986	−	4.34721i	0.104127	−	0.180353i
$582$	−31.1582	+	21.7089i	−1.29155	+	0.899864i
$583$		0			0
$584$	−38.5294			−1.59436
$585$	−0.968995	+	2.62409i	−0.0400630	+	0.108493i
$586$	−24.2984			−1.00376
$587$	−11.7762	−	20.3970i	−0.486056	−	0.841874i	0.513816	−	0.857901i	$-0.328232\pi$
$587$	−11.7762	−	20.3970i	−0.486056	−	0.841874i	−0.999872	+	0.0160270i	$0.994898\pi$
$588$	0.371760	+	4.36666i	0.0153311	+	0.180078i
$589$	11.4496	−	19.8312i	0.471771	−	0.817131i
$590$	−3.26489	+	5.65496i	−0.134414	+	0.232811i
$591$	−35.2227	−	16.5248i	−1.44887	−	0.679741i
$592$	6.69219	+	11.5912i	0.275047	+	0.476396i
$593$	13.1828			0.541354			0.270677	−	0.962670i	$-0.412752\pi$
$593$	13.1828			0.541354			0.270677	+	0.962670i	$0.412752\pi$
$594$		0			0
$595$	1.96270			0.0804630
$596$	0.223863	+	0.387742i	0.00916978	+	0.0158825i
$597$	−32.6613	−	15.3232i	−1.33674	−	0.627135i
$598$	−5.42055	+	9.38867i	−0.221663	+	0.383931i
$599$	−17.1082	+	29.6323i	−0.699022	+	1.21074i	0.269783	+	0.962921i	$0.413048\pi$
$599$	−17.1082	+	29.6323i	−0.699022	+	1.21074i	−0.968806	+	0.247821i	$0.920285\pi$
$600$	−1.69997	−	19.9677i	−0.0694009	−	0.815176i
$601$	−14.5143	−	25.1394i	−0.592049	−	1.02546i	−0.993956	−	0.109778i	$-0.964986\pi$
$601$	−14.5143	−	25.1394i	−0.592049	−	1.02546i	0.401907	−	0.915680i	$-0.368347\pi$
$602$	−4.70435			−0.191735
$603$	23.9249	−	4.10349i	0.974298	−	0.167107i
$604$	0.343924			0.0139941
$605$		0			0
$606$	31.5714	−	21.9968i	1.28250	−	0.893561i
$607$	1.57818	−	2.73348i	0.0640562	−	0.110949i	−0.832219	−	0.554447i	$-0.812930\pi$
$607$	1.57818	−	2.73348i	0.0640562	−	0.110949i	0.896275	+	0.443499i	$0.146263\pi$
$608$	2.73373	−	4.73495i	0.110867	−	0.192028i
$609$	−7.15996	+	4.98858i	−0.290136	+	0.202148i
$610$	−2.08655	−	3.61401i	−0.0844819	−	0.146327i
$611$	0.358392			0.0144990
$612$	−5.30263	+	0.909482i	−0.214346	+	0.0367636i
$613$	33.9410			1.37086			0.685432	−	0.728136i	$-0.259613\pi$
$613$	33.9410			1.37086			0.685432	+	0.728136i	$0.259613\pi$
$614$	2.71591	+	4.70409i	0.109605	+	0.189842i
$615$	0.100393	+	1.17920i	0.00404822	+	0.0475500i
$616$		0			0
$617$	10.8039	−	18.7129i	0.434948	−	0.753351i	−0.562344	−	0.826904i	$-0.690100\pi$
$617$	10.8039	−	18.7129i	0.434948	−	0.753351i	0.997291	+	0.0735523i	$0.0234336\pi$
$618$	−10.7374	−	5.03751i	−0.431923	−	0.202638i
$619$	−10.2563	−	17.7644i	−0.412235	−	0.714013i	0.582898	−	0.812545i	$-0.301919\pi$
$619$	−10.2563	−	17.7644i	−0.412235	−	0.714013i	−0.995134	+	0.0985323i	$0.968585\pi$
$620$	−2.11055			−0.0847617
$621$	22.3025	+	6.14372i	0.894970	+	0.246539i
$622$	40.7166			1.63259
$623$	−4.50507	−	7.80301i	−0.180492	−	0.312621i
$624$	11.4308	+	5.36282i	0.457600	+	0.214685i
$625$	−9.93266	+	17.2039i	−0.397306	+	0.688155i
$626$	1.90263	−	3.29545i	0.0760444	−	0.131713i
$627$		0			0
$628$	1.91094	+	3.30985i	0.0762550	+	0.132078i
$629$	13.2787			0.529456
$630$	0.686761	−	1.85979i	0.0273612	−	0.0740958i
$631$	29.8645			1.18889			0.594443	−	0.804138i	$-0.297372\pi$
$631$	29.8645			1.18889			0.594443	+	0.804138i	$0.297372\pi$
$632$	−18.1900	−	31.5060i	−0.723559	−	1.25324i
$633$	−4.82050	+	3.35860i	−0.191598	+	0.133493i
$634$	20.4918	−	35.4929i	0.813835	−	1.40960i
$635$	3.55110	−	6.15069i	0.140921	−	0.244083i
$636$	3.16552	−	2.20552i	0.125521	−	0.0874547i
$637$	−5.10193	−	8.83680i	−0.202146	−	0.350127i
$638$		0			0
$639$	−23.6046	−	28.3992i	−0.933784	−	1.12345i
$640$	7.96969			0.315030
$641$	19.0600	+	33.0129i	0.752826	+	1.30393i	0.946448	+	0.322856i	$0.104643\pi$
$641$	19.0600	+	33.0129i	0.752826	+	1.30393i	−0.193622	+	0.981076i	$0.562024\pi$
$642$	3.57668	+	42.0113i	0.141160	+	1.65806i
$643$	8.41257	−	14.5710i	0.331759	−	0.574624i	−0.651098	−	0.758994i	$-0.725691\pi$
$643$	8.41257	−	14.5710i	0.331759	−	0.574624i	0.982857	+	0.184370i	$0.0590245\pi$
$644$	0.627619	−	1.08707i	0.0247316	−	0.0428365i
$645$	−3.91247	−	1.83555i	−0.154053	−	0.0722747i
$646$	−8.90536	−	15.4245i	−0.350377	−	0.606870i
$647$	−20.9745			−0.824592			−0.412296	−	0.911050i	$-0.635273\pi$
$647$	−20.9745			−0.824592			−0.412296	+	0.911050i	$0.635273\pi$
$648$	4.09487	−	22.0185i	0.160862	−	0.864968i
$649$		0			0
$650$	−5.66102	−	9.80517i	−0.222043	−	0.384591i
$651$	−10.3337	−	4.84810i	−0.405010	−	0.190012i
$652$	−0.904049	+	1.56586i	−0.0354053	+	0.0613238i
$653$	−9.88324	+	17.1183i	−0.386761	+	0.669890i	−0.992012	−	0.126145i	$-0.959739\pi$
$653$	−9.88324	+	17.1183i	−0.386761	+	0.669890i	0.605251	+	0.796035i	$0.293073\pi$
$654$	3.11158	+	36.5483i	0.121672	+	1.42915i
$655$	2.03987	+	3.53316i	0.0797044	+	0.138052i
$656$	5.34191			0.208566
$657$	29.6910	+	35.7218i	1.15835	+	1.39364i
$658$	−0.254005			−0.00990215
$659$	5.90277	+	10.2239i	0.229939	+	0.398267i	0.957790	−	0.287469i	$-0.0928139\pi$
$659$	5.90277	+	10.2239i	0.229939	+	0.398267i	−0.727851	+	0.685736i	$0.759481\pi$
$660$		0			0
$661$	−8.90382	+	15.4219i	−0.346318	+	0.599841i	−0.985592	−	0.169138i	$-0.945902\pi$
$661$	−8.90382	+	15.4219i	−0.346318	+	0.599841i	0.639274	+	0.768979i	$0.279235\pi$
$662$	−6.26492	+	10.8512i	−0.243493	+	0.421742i
$663$	10.2779	−	7.16099i	0.399162	−	0.278110i
$664$	−8.65109	−	14.9841i	−0.335727	−	0.581497i
$665$	1.07222			0.0415789
$666$	4.64629	−	12.5824i	0.180040	−	0.487559i
$667$	−31.0688			−1.20299
$668$	3.31711	+	5.74540i	0.128343	+	0.222296i
$669$	1.62009	+	19.0294i	0.0626363	+	0.735720i
$670$	3.70329	−	6.41429i	0.143071	−	0.247806i
$671$		0			0
$672$	−2.46731	−	1.15755i	−0.0951784	−	0.0446533i
$673$	−9.85264	−	17.0653i	−0.379791	−	0.657818i	0.611240	−	0.791445i	$-0.290671\pi$
$673$	−9.85264	−	17.0653i	−0.379791	−	0.657818i	−0.991032	+	0.133627i	$0.957338\pi$
$674$	38.2215			1.47224
$675$	−17.2026	+	16.9633i	−0.662129	+	0.652916i
$676$	−4.10826			−0.158010
$677$	6.20696	+	10.7508i	0.238553	+	0.413185i	0.960299	−	0.278972i	$-0.0899937\pi$
$677$	6.20696	+	10.7508i	0.238553	+	0.413185i	−0.721747	+	0.692157i	$0.756660\pi$
$678$	19.4685	+	9.13372i	0.747683	+	0.350778i
$679$	−5.11880	+	8.86602i	−0.196441	+	0.340247i
$680$	3.38256	−	5.85877i	0.129715	−	0.224674i
$681$	0.876706	+	10.2977i	0.0335955	+	0.394609i
$682$		0			0
$683$	2.02837			0.0776135			0.0388068	−	0.999247i	$-0.487644\pi$
$683$	2.02837			0.0776135			0.0388068	+	0.999247i	$0.487644\pi$
$684$	−2.89681	+	0.496848i	−0.110762	+	0.0189974i
$685$	5.47425			0.209160
$686$	7.52274	+	13.0298i	0.287220	+	0.497479i
$687$	−35.1739	+	24.5068i	−1.34197	+	0.934994i
$688$	−9.75348	+	16.8935i	−0.371848	+	0.644060i
$689$	−4.49148	+	7.77947i	−0.171112	+	0.296374i
$690$	5.79137	−	4.03504i	0.220474	−	0.153611i
$691$	−1.17144	−	2.02899i	−0.0445635	−	0.0771862i	0.842883	−	0.538096i	$-0.180856\pi$
$691$	−1.17144	−	2.02899i	−0.0445635	−	0.0771862i	−0.887447	+	0.460910i	$0.847523\pi$
$692$	−0.230830			−0.00877483
$693$		0			0
$694$	−3.19995			−0.121469
$695$	−6.39729	−	11.0804i	−0.242663	−	0.420305i
$696$	2.55155	+	29.9703i	0.0967163	+	1.13602i
$697$	2.64986	−	4.58969i	0.100371	−	0.173847i
$698$	4.03098	−	6.98187i	0.152575	−	0.264268i
$699$	6.56768	+	3.08125i	0.248412	+	0.116544i
$700$	0.655461	+	1.13529i	0.0247741	+	0.0429100i
$701$	−4.43368			−0.167458			−0.0837289	−	0.996489i	$-0.526683\pi$
$701$	−4.43368			−0.167458			−0.0837289	+	0.996489i	$0.526683\pi$
$702$	−3.18919	−	12.2447i	−0.120368	−	0.462146i
$703$	7.25411			0.273594
$704$		0			0
$705$	−0.211249	−	0.0991082i	−0.00795609	−	0.00373263i
$706$	−16.7543	+	29.0193i	−0.630557	+	1.09216i
$707$	5.18669	−	8.98361i	0.195065	−	0.337863i
$708$	−0.409332	−	4.80797i	−0.0153836	−	0.180695i
$709$	−14.9413	−	25.8790i	−0.561131	−	0.971907i	−0.997398	−	0.0720902i	$-0.977033\pi$
$709$	−14.9413	−	25.8790i	−0.561131	−	0.971907i	0.436267	−	0.899817i	$-0.356300\pi$
$710$	−11.2676			−0.422864
$711$	−15.1929	+	41.1432i	−0.569777	+	1.54299i
$712$	−31.0565			−1.16389
$713$	−20.3195	−	35.1943i	−0.760970	−	1.31804i
$714$	−7.28435	+	5.07525i	−0.272610	+	0.189936i
$715$		0			0
$716$	1.88258	−	3.26072i	0.0703551	−	0.121859i
$717$	10.4778	−	7.30020i	0.391299	−	0.272631i
$718$	−6.76655	−	11.7200i	−0.252525	−	0.437387i
$719$	−21.6321			−0.806742			−0.403371	−	0.915037i	$-0.632162\pi$
$719$	−21.6321			−0.806742			−0.403371	+	0.915037i	$0.632162\pi$
$720$	−5.25473	−	6.32208i	−0.195832	−	0.235610i
$721$	−3.19741			−0.119078
$722$	9.82332	+	17.0145i	0.365586	+	0.633214i
$723$	1.29727	+	15.2376i	0.0482459	+	0.566691i
$724$	0.929846	−	1.61054i	0.0345574	−	0.0598552i
$725$	16.2235	−	28.1000i	0.602527	−	1.04361i
$726$		0			0
$727$	6.22109	+	10.7752i	0.230727	+	0.399631i	0.958022	−	0.286694i	$-0.0925561\pi$
$727$	6.22109	+	10.7752i	0.230727	+	0.399631i	−0.727295	+	0.686325i	$0.759223\pi$
$728$	2.82948			0.104868
$729$	−23.5695	+	13.1711i	−0.872946	+	0.487817i
$730$	14.1729			0.524561
$731$	9.67645	+	16.7601i	0.357897	+	0.619895i
$732$	2.79184	+	1.30980i	0.103189	+	0.0484117i
$733$	26.1761	−	45.3383i	0.966836	−	1.67461i	0.262238	−	0.965003i	$-0.415539\pi$
$733$	26.1761	−	45.3383i	0.966836	−	1.67461i	0.704598	−	0.709607i	$-0.251127\pi$
$734$	5.23075	−	9.05993i	0.193071	−	0.334408i
$735$	0.563566	+	6.61959i	0.0207875	+	0.244167i
$736$	−4.85153	−	8.40310i	−0.178830	−	0.309742i
$737$		0			0
$738$	−3.42183	−	4.11688i	−0.125959	−	0.151544i
$739$	−46.6760			−1.71701			−0.858503	−	0.512809i	$-0.828605\pi$
$739$	−46.6760			−1.71701			−0.858503	+	0.512809i	$0.828605\pi$
$740$	−0.334296	−	0.579018i	−0.0122890	−	0.0212851i
$741$	5.61482	−	3.91203i	0.206266	−	0.143712i
$742$	3.18327	−	5.51359i	0.116862	−	0.202410i
$743$	10.9359	−	18.9416i	0.401201	−	0.694900i	−0.592671	−	0.805445i	$-0.701926\pi$
$743$	10.9359	−	18.9416i	0.401201	−	0.694900i	0.993871	+	0.110545i	$0.0352597\pi$
$744$	−32.2812	+	22.4914i	−1.18348	+	0.824573i
$745$	0.339362	+	0.587793i	0.0124333	+	0.0215351i
$746$	−33.8501			−1.23934
$747$	−7.22567	+	19.5675i	−0.264373	+	0.715938i
$748$		0			0
$749$	5.68334	+	9.84384i	0.207665	+	0.359686i
$750$	1.29779	+	15.2437i	0.0473885	+	0.556621i
$751$	−19.7961	+	34.2878i	−0.722369	+	1.25118i	0.237679	+	0.971344i	$0.423613\pi$
$751$	−19.7961	+	34.2878i	−0.722369	+	1.25118i	−0.960048	+	0.279835i	$0.909720\pi$
$752$	−0.526627	+	0.912144i	−0.0192041	+	0.0332625i
$753$	32.2597	+	15.1348i	1.17561	+	0.551542i
$754$	8.49686	+	14.7170i	0.309437	+	0.535961i
$755$	0.521367			0.0189745
$756$	0.369260	+	1.41775i	0.0134299	+	0.0515631i
$757$	23.1457			0.841246			0.420623	−	0.907235i	$-0.361811\pi$
$757$	23.1457			0.841246			0.420623	+	0.907235i	$0.361811\pi$
$758$	26.1480	+	45.2896i	0.949736	+	1.64499i
$759$		0			0
$760$	1.84789	−	3.20063i	0.0670299	−	0.116099i
$761$	7.44643	−	12.8976i	0.269933	−	0.467538i	−0.698911	−	0.715208i	$-0.746332\pi$
$761$	7.44643	−	12.8976i	0.269933	−	0.467538i	0.968844	+	0.247671i	$0.0796651\pi$
$762$	2.72522	+	32.0102i	0.0987243	+	1.15961i
$763$	4.94429	+	8.56376i	0.178995	+	0.310029i
$764$	−2.03003			−0.0734438
$765$	−8.03846	+	1.37872i	−0.290631	+	0.0498477i
$766$	−28.4085			−1.02644
$767$	5.61755	+	9.72988i	0.202838	+	0.351325i
$768$	−12.8453	+	8.94973i	−0.463514	+	0.322946i
$769$	−10.8117	+	18.7264i	−0.389879	+	0.675290i	−0.992433	−	0.122788i	$-0.960816\pi$
$769$	−10.8117	+	18.7264i	−0.389879	+	0.675290i	0.602554	+	0.798078i	$0.294150\pi$
$770$		0			0
$771$	4.80681	−	3.34906i	0.173113	−	0.120614i
$772$	−0.638148	−	1.10531i	−0.0229675	−	0.0397808i
$773$	−6.07292			−0.218428			−0.109214	−	0.994018i	$-0.534833\pi$
$773$	−6.07292			−0.218428			−0.109214	+	0.994018i	$0.534833\pi$
$774$	19.2671	−	3.30461i	0.692543	−	0.118782i
$775$	42.4417			1.52455
$776$	17.6437	+	30.5597i	0.633371	+	1.09703i
$777$	−0.306737	−	3.60290i	−0.0110041	−	0.129253i
$778$	23.8156	−	41.2498i	0.853829	−	1.47888i
$779$	1.44761	−	2.50734i	0.0518661	−	0.0898347i
$780$	−0.571007	−	0.267890i	−0.0204453	−	0.00959200i
$781$		0			0
$782$	−31.6086			−1.13032
$783$	25.8201	−	25.4608i	0.922735	−	0.909896i
$784$	29.9874			1.07098
$785$	2.89688	+	5.01754i	0.103394	+	0.179084i
$786$	−16.7070	−	7.83814i	−0.595918	−	0.279577i
$787$	−25.5777	+	44.3019i	−0.911746	+	1.57919i	−0.100149	+	0.994972i	$0.531932\pi$
$787$	−25.5777	+	44.3019i	−0.911746	+	1.57919i	−0.811597	+	0.584218i	$0.801401\pi$
$788$	4.38625	−	7.59721i	0.156254	−	0.270639i
$789$	2.09847	+	24.6484i	0.0747075	+	0.877507i
$790$	6.69109	+	11.5893i	0.238058	+	0.412329i
$791$	5.79736			0.206130
$792$		0			0
$793$	−7.18019			−0.254976
$794$	6.41320	+	11.1080i	0.227596	+	0.394208i
$795$	4.79874	−	3.34344i	0.170194	−	0.118580i
$796$	4.06728	−	7.04474i	0.144161	−	0.249694i
$797$	12.6306	−	21.8769i	0.447399	−	0.774918i	−0.550817	−	0.834626i	$-0.685684\pi$
$797$	12.6306	−	21.8769i	0.447399	−	0.774918i	0.998216	+	0.0597082i	$0.0190170\pi$
$798$	−3.97942	+	2.77260i	−0.140870	+	0.0981489i
$799$	0.522468	+	0.904940i	0.0184836	+	0.0320145i
$800$	10.1335			0.358274
$801$	23.9323	+	28.7934i	0.845606	+	1.01737i
$802$	−6.08192			−0.214760
$803$		0			0
$804$	0.464295	+	5.45357i	0.0163744	+	0.192332i
$805$	0.951432	−	1.64793i	0.0335336	−	0.0580818i
$806$	−11.1141	+	19.2502i	−0.391479	+	0.678061i
$807$	10.5380	+	4.94394i	0.370955	+	0.174035i
$808$	−17.8777	−	30.9650i	−0.628935	−	1.08935i
$809$	51.3275			1.80458			0.902290	−	0.431130i	$-0.141885\pi$
$809$	51.3275			1.80458			0.902290	+	0.431130i	$0.141885\pi$
$810$	−1.50628	+	8.09939i	−0.0529252	+	0.284583i
$811$	4.54589			0.159628			0.0798138	−	0.996810i	$-0.474567\pi$
$811$	4.54589			0.159628			0.0798138	+	0.996810i	$0.474567\pi$
$812$	−0.983808	−	1.70401i	−0.0345249	−	0.0597989i
$813$	−6.24142	−	2.92819i	−0.218896	−	0.102696i
$814$		0			0
$815$	−1.37048	+	2.37375i	−0.0480059	+	0.0831487i
$816$	3.12287	+	36.6809i	0.109322	+	1.28409i
$817$	5.28622	+	9.15601i	0.184942	+	0.320328i
$818$	−3.87192			−0.135378
$819$	−2.18041	−	2.62330i	−0.0761897	−	0.0916654i
$820$	−0.266845			−0.00931864
$821$	−5.43690	−	9.41698i	−0.189749	−	0.328655i	0.755418	−	0.655244i	$-0.227434\pi$
$821$	−5.43690	−	9.41698i	−0.189749	−	0.328655i	−0.945167	+	0.326589i	$0.894101\pi$
$822$	−20.3171	+	14.1556i	−0.708639	+	0.493732i
$823$	11.8081	−	20.4522i	0.411604	−	0.712918i	−0.583462	−	0.812141i	$-0.698302\pi$
$823$	11.8081	−	20.4522i	0.411604	−	0.712918i	0.995065	+	0.0992224i	$0.0316355\pi$
$824$	−5.51048	+	9.54444i	−0.191967	+	0.332496i
$825$		0			0
$826$	−3.98136	−	6.89591i	−0.138529	−	0.239940i
$827$	−27.6040			−0.959886			−0.479943	−	0.877300i	$-0.659343\pi$
$827$	−27.6040			−0.959886			−0.479943	+	0.877300i	$0.659343\pi$
$828$	−1.80686	+	4.89308i	−0.0627926	+	0.170046i
$829$	−16.1009			−0.559208			−0.279604	−	0.960115i	$-0.590203\pi$
$829$	−16.1009			−0.559208			−0.279604	+	0.960115i	$0.590203\pi$
$830$	3.18226	+	5.51183i	0.110458	+	0.191318i
$831$	1.92947	+	22.6633i	0.0669324	+	0.786182i
$832$	4.63617	−	8.03008i	0.160730	−	0.278393i
$833$	14.8753	−	25.7648i	0.515399	−	0.892697i
$834$	52.3951	+	24.5814i	1.81429	+	0.851183i
$835$	5.02854	+	8.70968i	0.174020	+	0.301411i
$836$		0			0
$837$	45.7284	+	12.5969i	1.58061	+	0.435412i
$838$	16.6046			0.573596
$839$	9.71596	+	16.8285i	0.335432	+	0.580986i	0.983568	−	0.180539i	$-0.0577843\pi$
$839$	9.71596	+	16.8285i	0.335432	+	0.580986i	−0.648136	+	0.761525i	$0.724451\pi$
$840$	−1.66780	−	0.782453i	−0.0575445	−	0.0269972i
$841$	−9.85058	+	17.0617i	−0.339675	+	0.588334i
$842$	−17.1524	+	29.7089i	−0.591111	+	1.02383i
$843$	0.436064	+	5.12197i	0.0150189	+	0.176410i
$844$	−0.662357	−	1.14724i	−0.0227993	−	0.0394895i
$845$	−6.22787			−0.214245
$846$	1.04030	−	0.178428i	0.0357664	−	0.00613449i
$847$		0			0
$848$	−13.1997	−	22.8626i	−0.453280	−	0.785103i
$849$	−11.5009	+	8.01304i	−0.394709	+	0.275007i
$850$	16.5054	−	28.5882i	0.566131	−	0.980567i
$851$	6.43691	−	11.1491i	0.220655	−	0.382185i
$852$	6.83178	−	4.75993i	0.234053	−	0.163072i
$853$	9.89276	+	17.1348i	0.338722	+	0.586683i	0.984193	−	0.177102i	$-0.0566722\pi$
$853$	9.89276	+	17.1348i	0.338722	+	0.586683i	−0.645471	+	0.763785i	$0.723339\pi$
$854$	5.08886			0.174137
$855$	−4.39139	+	0.753191i	−0.150182	+	0.0257586i
$856$	39.1791			1.33912
$857$	2.17032	+	3.75911i	0.0741369	+	0.128409i	0.900711	−	0.434420i	$-0.143047\pi$
$857$	2.17032	+	3.75911i	0.0741369	+	0.128409i	−0.826574	+	0.562828i	$0.809713\pi$
$858$		0			0
$859$	2.58967	−	4.48545i	0.0883586	−	0.153042i	−0.818459	−	0.574565i	$-0.805171\pi$
$859$	2.58967	−	4.48545i	0.0883586	−	0.153042i	0.906817	+	0.421524i	$0.138505\pi$
$860$	0.487217	−	0.843885i	0.0166140	−	0.0287762i
$861$	−1.30653	−	0.612965i	−0.0445265	−	0.0208898i
$862$	14.2695	+	24.7154i	0.486019	+	0.841810i
$863$	−2.69392			−0.0917021			−0.0458510	−	0.998948i	$-0.514600\pi$
$863$	−2.69392			−0.0917021			−0.0458510	+	0.998948i	$0.514600\pi$
$864$	10.9182	+	3.00767i	0.371446	+	0.102323i
$865$	−0.349924			−0.0118978
$866$	−11.6862	−	20.2411i	−0.397113	−	0.687820i
$867$	6.40785	+	3.00626i	0.217622	+	0.102098i
$868$	1.28685	−	2.22889i	0.0436785	−	0.0756534i
$869$		0			0
$870$	−0.938574	−	11.0244i	−0.0318207	−	0.373762i
$871$	−6.37185	−	11.0364i	−0.215902	−	0.373953i
$872$	34.0843			1.15424
$873$	14.7366	−	39.9075i	0.498757	−	1.35066i
$874$	−17.2677			−0.584088
$875$	2.06218	+	3.57181i	0.0697145	+	0.120749i
$876$	−8.59332	+	5.98725i	−0.290341	+	0.202291i
$877$	10.4224	−	18.0521i	0.351939	−	0.609576i	−0.634650	−	0.772800i	$-0.718856\pi$
$877$	10.4224	−	18.0521i	0.351939	−	0.609576i	0.986589	+	0.163223i	$0.0521891\pi$
$878$	−18.5191	+	32.0761i	−0.624990	+	1.08251i
$879$	22.3339	−	15.5607i	0.753302	−	0.524851i
$880$		0			0
$881$	11.5843			0.390286			0.195143	−	0.980775i	$-0.437483\pi$
$881$	11.5843			0.390286			0.195143	+	0.980775i	$0.437483\pi$
$882$	−19.2089	−	23.1106i	−0.646796	−	0.778173i
$883$	15.3973			0.518159			0.259079	−	0.965856i	$-0.416581\pi$
$883$	15.3973			0.518159			0.259079	+	0.965856i	$0.416581\pi$
$884$	1.41223	+	2.44606i	0.0474985	+	0.0822699i
$885$	−0.620522	−	7.28859i	−0.0208586	−	0.245003i
$886$	−19.7115	+	34.1413i	−0.662220	+	1.14700i
$887$	2.95498	−	5.11817i	0.0992185	−	0.171851i	−0.812143	−	0.583459i	$-0.801699\pi$
$887$	2.95498	−	5.11817i	0.0992185	−	0.171851i	0.911361	+	0.411607i	$0.135032\pi$
$888$	−11.2835	−	5.29369i	−0.378649	−	0.177645i
$889$	4.33037	+	7.50043i	0.145236	+	0.251556i
$890$	11.4240			0.382932
$891$		0			0
$892$	−4.30623			−0.144183
$893$	0.285423	+	0.494367i	0.00955131	+	0.0165434i
$894$	−2.77945	−	1.30399i	−0.0929586	−	0.0436119i
$895$	2.85387	−	4.94305i	0.0953943	−	0.165228i
$896$	−4.85930	+	8.41655i	−0.162338	+	0.281177i
$897$	−1.03022	−	12.1009i	−0.0343982	−	0.404038i
$898$	17.3804	+	30.1038i	0.579993	+	1.00458i
$899$	−63.7025			−2.12460
$900$	−3.48201	−	4.18927i	−0.116067	−	0.139642i
$901$	−26.1909			−0.872546
$902$		0			0
$903$	4.32399	−	3.01267i	0.143893	−	0.100255i
$904$	9.99128	−	17.3054i	0.332305	−	0.575569i
$905$	1.40959	−	2.44148i	0.0468563	−	0.0811576i
$906$	−1.93500	+	1.34818i	−0.0642859	+	0.0447901i
$907$	3.69666	+	6.40280i	0.122746	+	0.212602i	0.920849	−	0.389918i	$-0.127497\pi$
$907$	3.69666	+	6.40280i	0.122746	+	0.212602i	−0.798104	+	0.602520i	$0.794163\pi$
$908$	−2.33030			−0.0773336
$909$	−14.9320	+	40.4367i	−0.495263	+	1.34120i
$910$	−1.04081			−0.0345025
$911$	7.09940	+	12.2965i	0.235214	+	0.407402i	0.959335	−	0.282271i	$-0.0910877\pi$
$911$	7.09940	+	12.2965i	0.235214	+	0.407402i	−0.724121	+	0.689673i	$0.757754\pi$
$912$	1.70602	+	20.0387i	0.0564918	+	0.663547i
$913$		0			0
$914$	−16.7675	+	29.0422i	−0.554620	+	0.960631i
$915$	4.23226	+	1.98558i	0.139914	+	0.0656413i
$916$	−4.83304	−	8.37107i	−0.159688	−	0.276588i
$917$	−4.97503			−0.164290
$918$	26.2687	−	25.9032i	0.866995	−	0.854932i
$919$	−41.6426			−1.37366			−0.686831	−	0.726817i	$-0.740999\pi$
$919$	−41.6426			−1.37366			−0.686831	+	0.726817i	$0.740999\pi$
$920$	−3.27943	−	5.68014i	−0.108120	−	0.187269i
$921$	−5.50882	−	2.58449i	−0.181522	−	0.0851617i
$922$	9.35693	−	16.2067i	0.308154	−	0.533739i
$923$	−9.69344	+	16.7895i	−0.319063	+	0.552634i
$924$		0			0
$925$	6.72247	+	11.6437i	0.221033	+	0.382841i
$926$	30.9703			1.01775
$927$	13.0953	−	2.24605i	0.430107	−	0.0737700i
$928$	−15.2098			−0.499286
$929$	17.0664	+	29.5598i	0.559930	+	0.969827i	0.997502	+	0.0706435i	$0.0225053\pi$
$929$	17.0664	+	29.5598i	0.559930	+	0.969827i	−0.437572	+	0.899184i	$0.644161\pi$
$930$	11.8745	−	8.27332i	0.389379	−	0.271293i
$931$	8.12634	−	14.0752i	0.266330	−	0.461297i
$932$	−0.817868	+	1.41659i	−0.0267901	+	0.0464019i
$933$	−37.4246	+	26.0750i	−1.22523	+	0.853656i
$934$	−4.69059	−	8.12434i	−0.153481	−	0.265837i
$935$		0			0
$936$	−11.5884	+	1.98759i	−0.378780	+	0.0649666i
$937$	51.6822			1.68838			0.844192	−	0.536041i	$-0.180081\pi$
$937$	51.6822			1.68838			0.844192	+	0.536041i	$0.180081\pi$
$938$	4.51596	+	7.82187i	0.147451	+	0.255393i
$939$	0.361612	+	4.24746i	0.0118008	+	0.138611i
$940$	0.0263067	−	0.0455645i	0.000858029	−	0.00148615i
$941$	−9.00309	+	15.5938i	−0.293492	+	0.508344i	−0.974633	−	0.223809i	$-0.928151\pi$
$941$	−9.00309	+	15.5938i	−0.293492	+	0.508344i	0.681141	+	0.732153i	$0.261484\pi$
$942$	−23.7260	−	11.1311i	−0.773035	−	0.362672i
$943$	−2.56907	−	4.44976i	−0.0836604	−	0.144904i
$944$	−33.0181			−1.07465
$945$	0.559776	+	2.14923i	0.0182095	+	0.0699143i
$946$		0			0
$947$	−14.3151	−	24.7946i	−0.465180	−	0.805715i	0.534030	−	0.845466i	$-0.320677\pi$
$947$	−14.3151	−	24.7946i	−0.465180	−	0.805715i	−0.999210	+	0.0397506i	$0.987344\pi$
$948$	−8.95281	−	4.20025i	−0.290774	−	0.136418i
$949$	12.1928	−	21.1186i	0.395796	−	0.685540i
$950$	9.01686	−	15.6177i	0.292546	−	0.506704i
$951$	3.89466	+	45.7462i	0.126293	+	1.48342i
$952$	4.12485	+	7.14445i	0.133687	+	0.231553i
$953$	16.6893			0.540620			0.270310	−	0.962773i	$-0.412874\pi$
$953$	16.6893			0.540620			0.270310	+	0.962773i	$0.412874\pi$
$954$	−9.16436	+	24.8176i	−0.296707	+	0.803500i
$955$	−3.07740			−0.0995822
$956$	1.43969	+	2.49361i	0.0465628	+	0.0806492i
$957$		0			0
$958$	−28.0414	+	48.5690i	−0.905975	+	1.56919i
$959$	−3.33778	+	5.78120i	−0.107782	+	0.186685i
$960$	−4.95333	+	3.45115i	−0.159868	+	0.111385i
$961$	−26.1624	−	45.3146i	−0.843948	−	1.46176i
$962$	−7.04160			−0.227030
$963$	−30.1916	−	36.3241i	−0.972911	−	1.17053i
$964$	−3.44815			−0.111058
$965$	−0.967394	−	1.67558i	−0.0311415	−	0.0539387i
$966$	0.730157	+	8.57635i	0.0234924	+	0.275940i
$967$	−12.1597	+	21.0612i	−0.391029	+	0.677281i	−0.992585	−	0.121549i	$-0.961214\pi$
$967$	−12.1597	+	21.0612i	−0.391029	+	0.677281i	0.601557	+	0.798830i	$0.294547\pi$
$968$		0			0
$969$	18.0632	+	8.47443i	0.580275	+	0.272238i
$970$	−6.49013	−	11.2412i	−0.208386	−	0.360934i
$971$	7.55191			0.242352			0.121176	−	0.992631i	$-0.461333\pi$
$971$	7.55191			0.242352			0.121176	+	0.992631i	$0.461333\pi$
$972$	−2.50826	−	5.54716i	−0.0804524	−	0.177925i
$973$	15.6023			0.500186
$974$	6.71404	+	11.6291i	0.215132	+	0.372619i
$975$	11.4826	+	5.38709i	0.367736	+	0.172525i
$976$	10.5507	−	18.2743i	0.337719	−	0.584947i
$977$	−1.01614	+	1.76001i	−0.0325093	+	0.0563078i	−0.881822	−	0.471582i	$-0.843683\pi$
$977$	−1.01614	+	1.76001i	−0.0325093	+	0.0563078i	0.849313	+	0.527890i	$0.177017\pi$
$978$	−1.05175	−	12.3537i	−0.0336313	−	0.395029i
$979$		0			0
$980$	−1.49797			−0.0478508
$981$	−26.2655	−	31.6006i	−0.838594	−	1.00893i
$982$	−51.3276			−1.63793
$983$	−16.7198	−	28.9595i	−0.533279	−	0.923666i	−0.999245	−	0.0388633i	$-0.987626\pi$
$983$	−16.7198	−	28.9595i	−0.533279	−	0.923666i	0.465966	−	0.884803i	$-0.345707\pi$
$984$	−4.08143	+	2.84367i	−0.130111	+	0.0906529i
$985$	6.64929	−	11.5169i	0.211864	−	0.366959i
$986$	−24.7736	+	42.9092i	−0.788953	+	1.36651i
$987$	0.233468	−	0.162665i	0.00743138	−	0.00517769i
$988$	0.771499	+	1.33628i	0.0245447	+	0.0425126i
$989$	18.7629			0.596624
$990$		0			0
$991$	40.1009			1.27385			0.636923	−	0.770927i	$-0.280207\pi$
$991$	40.1009			1.27385			0.636923	+	0.770927i	$0.280207\pi$
$992$	−9.94743	−	17.2294i	−0.315831	−	0.547036i
$993$	−1.19070	−	13.9859i	−0.0377858	−	0.443829i
$994$	6.87009	−	11.8993i	0.217906	−	0.377424i
$995$	6.16575	−	10.6794i	0.195468	−	0.338560i
$996$	−4.25792	−	1.99762i	−0.134917	−	0.0632970i
$997$	−8.06505	−	13.9691i	−0.255423	−	0.442405i	0.709588	−	0.704617i	$-0.248881\pi$
$997$	−8.06505	−	13.9691i	−0.255423	−	0.442405i	−0.965010	+	0.262212i	$0.915548\pi$
$998$	32.2785			1.02176
$999$	3.78717	+	14.5406i	0.119821	+	0.460044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.p.364.4		36
9.4	even	3		9801.2.a.cm.1.15		18
9.5	odd	6		9801.2.a.cp.1.4		18
9.7	even	3	inner	1089.2.e.p.727.4		36
11.5	even	5		99.2.m.b.58.8	yes	72
11.9	even	5		99.2.m.b.4.2	✓	72
11.10	odd	2		1089.2.e.o.364.15		36
33.5	odd	10		297.2.n.b.91.2		72
33.20	odd	10		297.2.n.b.37.8		72
99.5	odd	30		891.2.f.e.487.8		36
99.16	even	15		99.2.m.b.25.2	yes	72
99.20	odd	30		297.2.n.b.235.2		72
99.31	even	15		891.2.f.f.730.2		36
99.32	even	6		9801.2.a.cn.1.15		18
99.38	odd	30		297.2.n.b.289.8		72
99.43	odd	6		1089.2.e.o.727.15		36
99.49	even	15		891.2.f.f.487.2		36
99.76	odd	6		9801.2.a.co.1.4		18
99.86	odd	30		891.2.f.e.730.8		36
99.97	even	15		99.2.m.b.70.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.2	✓	72	11.9	even	5
99.2.m.b.25.2	yes	72	99.16	even	15
99.2.m.b.58.8	yes	72	11.5	even	5
99.2.m.b.70.8	yes	72	99.97	even	15
297.2.n.b.37.8		72	33.20	odd	10
297.2.n.b.91.2		72	33.5	odd	10
297.2.n.b.235.2		72	99.20	odd	30
297.2.n.b.289.8		72	99.38	odd	30
891.2.f.e.487.8		36	99.5	odd	30
891.2.f.e.730.8		36	99.86	odd	30
891.2.f.f.487.2		36	99.49	even	15
891.2.f.f.730.2		36	99.31	even	15
1089.2.e.o.364.15		36	11.10	odd	2
1089.2.e.o.727.15		36	99.43	odd	6
1089.2.e.p.364.4		36	1.1	even	1	trivial
1089.2.e.p.727.4		36	9.7	even	3	inner
9801.2.a.cm.1.15		18	9.4	even	3
9801.2.a.cn.1.15		18	99.32	even	6
9801.2.a.co.1.4		18	99.76	odd	6
9801.2.a.cp.1.4		18	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.773068 - 1.33899i) q^{2} +(1.56806 + 0.735660i) q^{3} +(-0.195269 + 0.338216i) q^{4} +(-0.296016 + 0.512715i) q^{5} +(-0.227172 - 2.66833i) q^{6} +(-0.360975 - 0.625227i) q^{7} -2.48845 q^{8} +(1.91761 + 2.30711i) q^{9} +0.915362 q^{10} +(-0.555005 + 0.386690i) q^{12} +(0.787482 - 1.36396i) q^{13} +(-0.558117 + 0.966687i) q^{14} +(-0.841354 + 0.586199i) q^{15} +(2.31428 + 4.00845i) q^{16} +4.59200 q^{17} +(1.60677 - 4.35122i) q^{18} +2.50860 q^{19} +(-0.115606 - 0.200235i) q^{20} +(-0.106075 - 1.24595i) q^{21} +(2.22600 - 3.85554i) q^{23} +(-3.90203 - 1.83065i) q^{24} +(2.32475 + 4.02658i) q^{25} -2.43511 q^{26} +(1.30967 + 5.02840i) q^{27} +0.281949 q^{28} +(-3.48931 - 6.04366i) q^{29} +(1.43534 + 0.673395i) q^{30} +(4.56412 - 7.90529i) q^{31} +(1.08974 - 1.88749i) q^{32} +(-3.54993 - 6.14866i) q^{34} +0.427418 q^{35} +(-1.15475 + 0.198058i) q^{36} +2.89170 q^{37} +(-1.93932 - 3.35900i) q^{38} +(2.23823 - 1.55945i) q^{39} +(0.736620 - 1.27586i) q^{40} +(0.577060 - 0.999497i) q^{41} +(-1.58631 + 1.10524i) q^{42} +(2.10724 + 3.64985i) q^{43} +(-1.75053 + 0.300244i) q^{45} -6.88340 q^{46} +(0.113778 + 0.197069i) q^{47} +(0.680067 + 7.98800i) q^{48} +(3.23939 - 5.61079i) q^{49} +(3.59438 - 6.22565i) q^{50} +(7.20052 + 3.37815i) q^{51} +(0.307542 + 0.532678i) q^{52} -5.70359 q^{53} +(5.72053 - 5.64093i) q^{54} +(0.898268 + 1.55585i) q^{56} +(3.93363 + 1.84548i) q^{57} +(-5.39495 + 9.34433i) q^{58} +(-3.56678 + 6.17784i) q^{59} +(-0.0339715 - 0.399026i) q^{60} +(-2.27948 - 3.94817i) q^{61} -14.1135 q^{62} +(0.750262 - 2.03175i) q^{63} +5.88733 q^{64} +(0.466215 + 0.807507i) q^{65} +(4.04571 - 7.00738i) q^{67} +(-0.896676 + 1.55309i) q^{68} +(6.32686 - 4.40814i) q^{69} +(-0.330423 - 0.572310i) q^{70} -12.3094 q^{71} +(-4.77187 - 5.74113i) q^{72} +15.4833 q^{73} +(-2.23548 - 3.87196i) q^{74} +(0.683144 + 8.02414i) q^{75} +(-0.489852 + 0.848448i) q^{76} +(-3.81839 - 1.79141i) q^{78} +(7.30978 + 12.6609i) q^{79} -2.74025 q^{80} +(-1.64555 + 8.84829i) q^{81} -1.78443 q^{82} +(3.47650 + 6.02148i) q^{83} +(0.442113 + 0.207419i) q^{84} +(-1.35931 + 2.35439i) q^{85} +(3.25808 - 5.64316i) q^{86} +(-1.02536 - 12.0438i) q^{87} +12.4803 q^{89} +(1.75531 + 2.11185i) q^{90} -1.13705 q^{91} +(0.869338 + 1.50574i) q^{92} +(12.9724 - 9.03831i) q^{93} +(0.175916 - 0.304695i) q^{94} +(-0.742586 + 1.28620i) q^{95} +(3.09733 - 2.15801i) q^{96} +(-7.09023 - 12.2806i) q^{97} -10.0171 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} - q^{6} - q^{7} - 12 q^{8} - q^{9} - 4 q^{10} - 8 q^{12} - 3 q^{13} - 5 q^{15} + 8 q^{16} - 40 q^{17} + 17 q^{18} - 6 q^{19} + 5 q^{20} - 8 q^{21} + 10 q^{23}+ \cdots - 164 q^{98}+O(q^{100}) \) 36 * q + 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 - q^6 - q^7 - 12 * q^8 - q^9 - 4 * q^10 - 8 * q^12 - 3 * q^13 - 5 * q^15 + 8 * q^16 - 40 * q^17 + 17 * q^18 - 6 * q^19 + 5 * q^20 - 8 * q^21 + 10 * q^23 - 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 + 38 * q^28 + 21 * q^29 + 12 * q^30 - 6 * q^31 + 9 * q^32 + 4 * q^34 - 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 + 42 * q^39 + 20 * q^41 + 18 * q^42 - 4 * q^43 + 20 * q^45 + 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 + 25 * q^50 - 4 * q^51 + 19 * q^52 + 62 * q^53 + 17 * q^54 + 57 * q^56 - 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 + 16 * q^61 - 38 * q^62 + 5 * q^63 - 32 * q^64 + 42 * q^65 + 5 * q^67 + 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 + 51 * q^72 + 9 * q^74 - 16 * q^75 + 8 * q^76 - 32 * q^78 + 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 + 36 * q^83 + 60 * q^84 - 25 * q^85 - 26 * q^86 - 60 * q^87 - 28 * q^89 + 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 - 4 * q^94 + 64 * q^95 - 21 * q^96 + 16 * q^97 - 164 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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